So after most of a year here in Rome, I'm prepared to share my accumulated wisdom about riding the buses here, for the edification of anyone who might find it helpful. After all, many will be descending on Rome in these days, and surely some will have the privilege of adventuring on her buses.
First, to travel by bus you must get on the bus. This is easier than it might appear, because there is no such thing as entrance and exit doors. Perhaps someone would point out that some of the doors are labeled with inviting forward arrows and others with forbidding 'do not enter' bars, but like a great many things that might seem to be clearly and obviously signified in Rome, these signs are only there as decoration and are not meant to have significance for anyone's life-choices.
Seeing as you are taking the bus, you may or may not wish to pay a fare. Unless you are in Rome for a very short visit, you are expected to either cheat or have a pass. People having to validate the single-use tickets on the bus is a hassle for everyone. Generally speaking, the passes are a good deal. The one that lasts a whole year is the best deal of all, though I understand that it inflicts on its bearer a diffuse but nevertheless near-unmanageable sense of post-modern dread.
If you do happen to be using the single-trip ticket, you don't need the validating machine anyway. You can validate the ticket yourself by simply writing the current time on the back. (N.B. It's probably better not to do this if you plan on trying to use the same ticket to transfer into the subway.) This procedure makes your ticket valid enough such that, in a raid, you will probably get out of being fined. Just say that you couldn't get to the machine or you thought it was broken.
This brings us to raids. Once in a while, officials will board the bus to check on who has paid a fare and who hasn't, offering to the latter the punishment of fines to be paid. If you have paid a fare, you are invited to relax and enjoy the scene. In fact, this show is one of the best things you have paid for in buying your bus ticket or pass. That's why the passes are called abbonamenti, a word that usually translates to 'subscription' in English.
If you have not paid a fare, you may wish to try to get out of being fined. If you are either young enough or youthful enough in appearance to be called a ragazza, you can get out of the fine by crying. Note that this strategy will be counterproductive for any other sort of person. Otherwise, the best way to try to get out of a fine is to loudly and passionately proclaim why you should not be fined. The loudness is so that other passengers can take your side and make the ticket-checking official afraid or ashamed. Keep in mind that passion, volume and showmanship are what matter here, not whether the excuse is legitimate or even makes any sense. Note that this procedure is only advisable when one can be confident that his fellow passengers already feel ill-served by an overcrowded bus and will be happy to have an opportunity to rail against authority.
It is not an absolute moral imperative that you offer your seat to someone who is your senior, but you should, if only to make sure people don't think that your mother didn't teach you any manners, you lout. You are to offer your seat to a woman religious, of any age, who doesn't have one. She is supposed to graciously accept. You are also to offer your seat to a male religious or priest of any age, but he is supposed to graciously decline. If he accepts, it has to be because he is older than you, not because he is a religious and/or a cleric.
Finally, the all-important act of getting off the bus. I say 'all-important' because the proper execution of your exit from the bus should preoccupy you for the entire trip. Indeed, your primary task in riding the bus is to position yourself such that you will be the first in line at the door when the bus arrives at your stop. In fact, this matters so much that you must try to get to the position of first in line a stop or two before your stop, just so you're ready to go. The fact that everyone trying to do this at once produces gridlock at best--if not a small-scale state of Hobbesian warfare--ought not to trouble you, however. In fact, it is all the more reason to make every effort to execute this last procedure perfectly.