I would imagine the bus companies have rules like that for a long-haul trip, but I do not know. You could probably contact a person who sells the tickets (like Astrid of Superior Tours).
I take my dogs on leash on the city buses, but I would not want to take them on a 5 hour trip on a public bus without have a crate to put them in. This is for the safety of the dog and the passengers. If something happened and the dog panicked and got away, it could mean big problems.