Our bus systems in the area where I live and work in North Carolina won't allow bikes inside the bus unless they are folding bikes. And, they are supposed to be covered (in a bag). However, I've seen many times where the bus drivers don't care if the folding bike isn't covered. I've also seen where pretty young women have been able to bring their non-folding bikes on board. I've never had that luxury offered to me with my bike when the rack was full...
As for bringing a full size bike on board: If nobody needs the handicapped seating area, just fold up the seat and stand there holding the bike. On a recent trip to Belgium, the city buses in Charleroi did not have racks on the exterior, but did allow bikes on the bus. They had an area where a couple of benches had been removed and it was for anything: Bikes, wheelchairs, people just standing (as I was).
There are some bus racks that my Fuji "Touring" will not fit in. The wheelbase is just an inch or so too long. Those racks are on some of the older buses. Newer buses with newer racks accept the Fuji.
Having said that, there is one rack company, "Sportworks" that make the racks currently used on the buses. One type of rack has never been a problem for me. The other has allowed my bike to "almost" completely leave the bus... In both cases, the driver stopped quickly enough for me to rescue the bike. The type of rack that has proven a problem is the type that does not have the "loop" of metal that surrounds the rear wheel. If the spring-loaded hook over the front wheel is a little weak and the bike starts bouncing around, the front wheel can come up and over the "chock". And since the rear wheel has no "chock" behind it, the bike can separate from the bus. Solving this is easy: Remove the heavier pannier from the bike to get rid of weight on the rear. Also, I place a bungee on the front axle and under the rack. I also place a bungee under the rack and up to the chain stays. I never had this problem on the buses with racks that have the metal material that completely "chocks" the wheels. Oh well.
Look at the photo above in a previous response. It's a triple rack. The position closest to the bus has NO WHEEL CHOCK at all! Bizarre! Also, you can see how the metal frame of the rack doesn't completely surround the front wheel of the bike as the two other positions do. However, the two other positions have both a wheel chock for the front wheel and the metal does not dip down and leave the rear wheel "open." The metal frame continues to loop behind the rear wheel and creates a chock. I much prefer the middle and front type of rack as opposed to the one closest to the bus. That looks quite sketchy without any type of wheel chock.