Living in
Human Shield: If you're lucky enough to be walking close to someone, position yourself so that they're in-between you and the bum. It's now their problem to deal with. Once in position, keep your eye on the shield. A clever shield will sometimes pull a counter maneuver on you, abruptly slowing down and veering away when you reach the bum, leaving you in the line of fire.
Cell phone force field: If you're talking on the phone you are surrounded by an invisible force field that allows you to completely block out the world. It would be rude of you to not give the person you're on the phone with your undivided attention, and even ruder for a stranger to try to interrupt you.
1,000 yard stare: You take on the vacant stare of a veteran traumatized by combat. You're too busy looking in the distance for insurgents to notice the spanger.
Confrontation: If you see the same bums everyday this might be the best solution of all. I've not tried it myself but my friend Keri at the breakfast place I go to every morning swears by it. Just walk up and give the bum a piece of your mind. "Look, I work too hard for my money to just give it away to lazy bums. Get a job!". While this may be difficult for some of you to do, consider it a long term investment. Instead of having to deal with the same person every single day you only have to deal with them once.
The crazy: Being crazy sucks, but one side benefit is that people tend to leave you alone. As you approach the bum, he'll be thinking of a way to start a conversation. Beat him to the punch and start one with yourself first. My friend Mac is a master of this technique. I think it's because it allows him to let out some of the crazy he keeps bottled up inside while performing his duties as a sane person.