I bird on my own nearly all the time, and I never give personal safety a second thought in most areas. In areas, though, where I know there have been past or current problems (but the birds are just too good to miss!), I use a bit of theater, too:
Attitude! It's worked for me when traveling abroad and in certain areas in LA, even when shopping during the day. While I've never had an unsavory incident while birding anywhere in the world, if I were on my own and someone happened on the scene that made my antennae start waving around, I'd do what I do in the city and somebody bugs me: Immediately go into "meaner'n snake poo-poo" mode. Meaning, I don't act, look, or sound pleasant, and I
always look the newcomer straight in the eye -- not in challenge, but just to let them know I know they're there and I know what they look like and I'm not afraid of them. Not that that'll deter *all* the baddies out there, but if you don't look or act like a potential victim, chances are favorable you won't end up being one. But I'm a brazen ol' broad sometimes so it works for me.
However, common sense always rules, so if the person who made my hackles rise looks like the "looking nasty bluff" won't be very effective, I just leave as unobtrusively and casually as possible. As others have already said, being alert is the best first line of defense.
Cel phone is an absolute must, but I never leave home without it anyway, even just for the odd grocery trip. What did we ever do before them?