'go for a ride on a bike/motor bike/scooter'
'go for a ride on a horse'
'go for a ride on a carousel'
'go for a drive in a car'
'go for a ride in a bus' ?? sounds a little odd, because 'go for a ride' suggests a recreational activity and maybe not following a set route, whereas going by bus, or taking or catching a bus, is normally to get from a to b.
I agree with waltern, you can also say 'go for a ride in a car'.
You can also go for a ride in a bus, if your objective is not so much to get from A to B, but rather to enjoy the bus ride itself. Here in Australia when it gets hot I sometimes go for a ride on a bus - any bus - just to enjoy the air conditioning!