They are both acceptable and mean the same thing in American English.Do sentences "The children are riding the bus" and "The children are riding on the bus" have the same meaning?
'the bus', 'in the bus', 'on the bus' ---- it doesn't make much difference, does it? -----unless you want to clarify that they are not riding on the roof of the bus.
In most cases we'd say: "The children are taking the bus" whether or not they are inside at present or will be at some time in the future.
The first sentence, without 'on', is unnatural in BrE.