Depends on a few things. Such as what type of bus, whether there is enough room for it to safely pass. Minibuses such as the access a ride bus need less room to safely pass then say an MTA bus. Keep in mind buses have large blind spots so you need to give it more room so it can see you in the mirrors when it passes you. Also if the avenue has two or more lanes you should be in the rightmost one. If a vehicle that you can't share the road with tries to pass you take the lane and force it to pass you. You really should have no cause for concern about oncoming busses in the opposite direction unless they frequently come into your lane. In which case you need to find a new route ASAP!

What avenue are you taking? It sounds like there is a lot of heavy vehicle traffic on it. You might be better off taking another avenue or a side street.