Let's talk about insulation!
First off, let's just acknowledge that insulation (like almost everything else on a skoolie) is a matter of personal preference. If you've got some hair-brained, never-been-tried idea to insulate your bus, I say give it a shot! Don't want to insulate at all? It's your bus, and you can try what you want!
This post is just to give you some options that seem to be the most often recommended in the world of skoolies.
Second point - insulating your bus is of course about keeping the bus warm in the winter and cool in the summer...but it's ALSO about keeping condensation to a minimum in the winter. So creating a thermal break is just as important! Note: having a wood stove in the bus drastically helps with condensation issues, so if you're planning on a wood stove, rather than propane heat, you don't need to be quite so paranoid about the thermal bridge issue. An externally vented propane heater also would help solve this problem.
Third point - if you keep all your original windows (like I'm planning on doing) recognize that you're going to lose a TON of heat through them in the winter, and let in a TON of heat in the summer. You can tint them to help a small amount in the summer, but just realize that even if you insulate the heck out of everything else, you'll still need to compensate with some pretty good heating if you keep all the windows.
Prepping the floor
Most (not all) school buses have a metal floor underneath a layer of rubber/linoleum or else rubber/linoleum+wood. If that's the case for you, strip the floor down the metal (use wire brush, wire wheel, etc), treat with a rust converter like OSPHO, then fix/patch any holes.
There are multiple ways to patch. Best option is probably to weld the holes closed, but here are a few other options:
Use butyl caulk (probably not as good of an idea to use silicon, since it can contain an acid for the curing process which may react with the metal). Plastic vehicle retainer clips make good cheap plugs you can stuff in the holes with the caulk.
You can cut out small metal patches and use 2-part epoxy to secure them
Use aluminum tape (hey, it's flat and strong)
Quick Steel - epoxy putty - hardens in an hour and can be sanded/filed/painted
Once you finish the patching, prime, and paint the floor then you're ready to insulate!
Framing the floor
Some people frame out the floor before putting down rigid foam insulation. Personally, I don't see the point since the rigid foam will be covered with plywood, which will distribute the weight, and 25psi rigid foam is PLENTY strong to support whatever you place on top of it, as long as the weight is distributed (which the plywood takes care of). Actually, even 15psi would be plenty. Think of it this way, even 15psi foam will support over 2,000lbs per square foot! But if you really, really want to, just use some 2x2's, or 2x4's as sleepers to frame out sections of the floor.
Almost without exception, rigid foam insulation is what people use for the floor, so I won't even discuss other options here. I'd recommend at least 1", more if you're willing to give up more headroom.
To attach, just use an adhesive (Loctite PL would my recommendation) one tube for each 4x8 sheet of insulation. Weigh it down (sand bags work well) and allow it to dry. Using only adhesive means you're not going to put any new holes in that floor you just patched, AND you didn't create any thermal bridge with fasteners, so double win! I'd recommend you tape the seams with aluminum tape as well.
I'd recommend 3/4 plywood - tongue and groove would work well. Use the same technique as the installation, securing it with a tube of Loctite PL for each 4x8 sheet. You'll end up with a very secure floor, and no holes through the metal floor of the bus. Once you have the plywood down, just install your choice of flooring on top!
Here's what your floor sandwich should look like:
The Walls & Ceiling
There are two really good main options here: use rigid foam board again, or go with closed-cell spray foam. There are other options as well—I've seen people use denim or fiberglass insulation for instance—but the best bang for your buck is going to be the first two options.
For either option, you'll want to attach wooden furring strips to the bus first, then insulate out flush with the furring strips. Keep the furring strips thin if you're trying to maximize space (particularly headroom) in the bus, or use thicker ones if you want more insulation. Screw the furring strips into the bus ribs with self-tapping screws (you'll probably need to pre-drill the holes) and counter sink the screws. You'll cover these screws later when you install your ceiling/walls, which will eliminate the thermal bridge that would otherwise be created by the screws.
Want to take it a step further? Install a thermal break between the ribs and the furring strips (since wood still conducts heat) by putting in 1/2" rigid foam strips on the ribs (just fasten them with a couple of screws) then attach the furring strips, screwing through the foam. Your screws will still conduct some heat/cold, but not nearly as much as having the furring strips right on the ribs. Note that this option is not pictured in the diagram above.
Wondering what to do about that metal ledge (the chair rail) that sticks out a few inches, about a foot off the floor ? Leave that, it's structural. If you can spare the space, insulate out flush with that ledge, cover it with a thin thermal break of some sort, and panel over the whole thing. If you don't insulate out that far, it might still collect moisture, but not the end of the world. Plus it makes a great anchor to bolt furniture or other structures to.
DON'T FORGET! Make sure to run any conduit for wires you want behind the walls before you start insulating!
Option 1: Rigid foam board
Cut it to fit into the spaces between ribs, scoring the back of it if necessary to bend it for ceiling curves. Cut thin wedges to jam into any remaining spaces. If you need adhesive, Loctite PL is a great option. If you're going to use a can of spray foam to fill in gaps, make sure you pick something that's closed-cell, rather than open-cell (which can hold in moisture). Cost wise, this usually ends up being a little cheaper than spray foam, although you'll end up with a slightly lower R-value insulation per inch.
Types of Rigid Foam:
Expanded polystyrene (EPS) White, the cheapest option, but fragile, and not a moisture barrier. Lowest R value, at about R-4 per inch.
Extruded polystyrene (XPS) Blue, green, or pink, and about 2x the cost of EPS. About R-5 per inch, and considered a moisture retarder.
Polyisocyanurate (ISO) The most expensive (about 3x the cost of EPS), but with an aged R value of about R-6.5 per inch. It starts out at around R-8, but degrades over time. Can be foil faced (creates moisture barrier) or paper faced (no barrier).
Option 2: Closed-cell spray foam
This is the best option - besides not needing a moisture barrier and giving you complete coverage over the walls, ribs, etc, this will give you the highest R-value with R-7 per inch. You can hire this out (sometimes if you offer to bring the bus to the location where a house is already being spray foamed, you can get a better price). It may be cheaper to do it yourself, using one of the popular "Foam it Green" kits—but the savings may or may not be worth it to you. Call around first, and see how much an installer would charge—I've seen some people reporting deals that cost basically the same as doing it yourself!
A 40ft bus in the ballpark of 560sq feet of ceiling and walls (assuming up to 3ft height below the windows). So the Foam it 602 kit will give you about 1" of depth on a full 40ft flat nose.
Covering the Insulation
For ceiling & walls, most people either use thin sheets of plywood (also called lauan) that's 1/8" thick. Screw that to the furring strips. Make sure your screws aren't too long—you don't want them to touch the ribs of the bus, and create a thermal bridge. If you do, in the winter you might get condensation dripping off each exposed screw head. You might choose to run a trim piece to cover the joints between panels. It can be difficult to get the lauan to follow the curve of the roof.
Alternatively, run tongue and groove boards the length of the bus, again connecting into the furring strips that you installed before insulating, making sure not to screw through the furring strips into the ribs.
Have some other wall/ceiling covering in mind? Go for it! Just try not to create any thermal bridges by having a metal pathway the cold can follow from the outside skin of the bus to the interior—so avoid screws that touch the ribs, and are exposed to the inside air of the bus.
What about a moisture barrier?
The idea behind a moisture barrier on the bus is to keep the warm, moist air from coming in contact with the cold steel of the bus (which would create condensation, possibly soaking into your insulation/wood siding, etc). So for your floor, if you taped the seams of your foam core, you're probably good. Want to add an extra layer of moisture barrier in there? Probably won't hurt anything so feel free. Some will argue that it creates an area between the moisture barrier and the steel floor (which also acts as a moisture barrier) where if water DOES get in there it can't escape or evaporate. So take that for what it's worth. Personally, I'm not planning on installing a moisture barrier in the floor.
For the walls/ceiling, if you used spray foam, it is already a moisture barrier, no need for anything else. If you use rigid foam, again, just tape your seams, make sure all the metal is covered and you should be golden. Didn't cover all your metal with insulation? There's an argument there for adding a moisture barrier on top of or behind your insulation. However, note that if you're keeping your windows, you're gonna have the window frames already collecting moisture, so trying to eliminate all condensation with just a moisture barrier is probably futile. Air flow, and a good heat source are probably a better plan.
As far as a moisture barrier to keep exterior moisture from coming into your living space from outside (like you'd have on a house) your steel bus is already a moisture barrier.