I have moved my entire household including cages with birds between cities. The birds do NOT stay on their perches. The motion of the vehicles is so unnatural and extreme that they hunker down on the bottom of their cages and weather the storm.
Granted, intelligence would help considerably. Obviously the wind whips branches around, but have you ever noticed trees moving visibly in the wind tend to be devoid of birds? Their claws really aren't built to handle the upside-down pendulum force of their bodies being whipped around.
The top of the bus is absolutely the worst possible place for them. It's the most dangerous and the most difficult to hang on to. There's a reason you don't see open-top buses anywhere but as local tour buses and in amusement parks. Top speed is about 35 mph. You'd have to slow that to about 15 mph to keep the avioids safe.
We're all assuming claws, not feet (therefore not really humanoid). If they have feet, there's a serious problem. If they have claws, then use hydraulics to open the top of the bus like the space shuttle hangar doors to give them access to the protected interior.
The perches need to be near the floor, as in only high enough to let claws wrap comfortably around them (maybe 8 inches to center of a 5 inch radius cylindrical perch). They can be retracted into the floor with a seat that can be raised or lowered like a hide-a-bed to make the space available for the avioids, their wings, and their parcels.
Just as with humans, they need either rails in front of them to hold on to or hand-straps hanging from the ceiling (which opens...). That sway is hard enough for humans who can shuffle their feet in either the X or Y planes. Aviods with claws only have the X plane to work with (which is a huge reason why my birds were on the floor of their cages).
In this case, your biggest problem is how to get them out of the bus without seriously inconveniencing other passengers. There may need to be rungs up the side of the bus (perhaps on the bottom of the hide-a-seat) that would let the birds climb to the open roof to stretch their wings and leap.
One last thing... while an imaginative engineer might figure out a way to let humans and really big birds cohabit the same coach space, in reality their needs are so very different that it's impractical to do it. In the end, you'd probably have busses and train cars dedicated to each species. After all, you'd be just barely inclined to forgive the fat, smelly dude taking the last open seat next to you, but the first time feathers brushed your hair or a wing smacked you on the head as the avioid soared into the air... you'd be complaining to your city council.