This has been discussed on another thread and I didn't want to hijack it. This is how I built mine.
Off the top of my head I can't think of any RE school bus with the exception of a Crown or Gillig mid-engine bus that doesn't have the frame rails extending to the rear bumper.
I have a 91 Bluebird AARE. It has a frame going all the way to the rear bumper but, it isn't the main frame. The main frame stops about 3 feet from the rear there is another. My understanding is this was done to lower the engine.
Because of the rear overhang I didn't want my receiver below the bumper so I built mine into the rear bumper. The bumper isn't all that strong laterally, it flexes a lot, so I added a reinforcement to the back side. I then tied it to the crossmember the engine sits on. I don't think this arrangement would be suitable for a large trailer with a lot of tongue weight. It is more than enough for the small trailer I sometimes pull and towing "4" down where there is no tongue weight, only pull.
Finished receiver mounted in bumper
Angle welded to back side of bumper to give lateral stability. This piece spans almost the width of the frame.
Grade 8 bolts (with spacers) that tie hitch to the engine crossmember to add more lateral strength.
For those who have a bus with separate turn signals and brake lights there are a couple of ways to get your lights to work. On my towed I added an extra bulb in the tail light assy. this entails making a hole in the back of the tail light assy. and adding an extra wire. I did it this way because my towed brake controller needs a separate brake light. For this setup I use a 7 wire trailer connector.
For my trailer I built a converter. This can be done for a few dollars using three relays. The switch is to turn it off so the relays aren't working when I'm not pulling the trailer. For this setup I use a standard 4 wire trailer connector.
Here's a wiring diagram.