The word "садиться" means "to board" in that sentence. So it's a process. I would translate is as "The driver offered them to start boarding."

If the driver asked someone to "sit down" it would be "Шофёр предложил им сесть." That would mean "The driver offered them to take a seat (when already on the bus)".

By the way, the perfective of сидеть and садиться is the same -- сесть.
So you can say "Шофёр предложил им сесть в автобус." The driver offered them to hop on the bus (i.e. to give them a ride). Here the result of giving them a ride is more important, hence the perfective. That's the version that you had in mind when you asked you question. Yet, it's also possible.