Actually, the word has a curious resonance in that it's an insult to both sexes, but in a different way: applied to a woman, it means she's not womanly, applied to a man, it's that he's going to be anally raped and used as a servant.... that is, as a woman.
In Scots, you can call either gender a bitch, but it's (apparently) less an insult than a coarse term of endearment: Lord Kames, Henry Home, Scots humanist and hangin' judge (now that's an oxymoron...true though) used it habitually to greet friends ("brute" was another Homesism...you can tell I like this guy...) to such an extent that his parting speech on leaving the bench at the age of 86, suffering from terminal cancer, ended with a cheery "Fare ye weel, ye bitches!".
Somewhere in between, in current street lingo, at least where I am, it's used as a near-synonym for "woman". I can't but wonder whether the fact that Southern English, which is a major influence on Ebonics, is based on Ulster Scots is one of the reasons for this casual attitude...or is it just the effort to sound tough? Used by a woman, it's pretty much one of the most empowering words on earth: you can't be called a bitch in turn if you've already proven that you are one by calling someone else one!
Anyway, the line between the classes on this is firm. In my own life, I used the word (in the street sense) to my yuppie step-sister-in-law, who was, at the time, a teacher in a reform school, at a Christmas Eve party. She had been spending much of her time bitterly decrying such crimes against humanity as the popularity of Beavis and Butthead, the (to me, willful, but to her, shocking) ignorance of her pupils, and the like.... in short, why couldn't she be teaching blonde, blue-eyed, WASPs in an evangelical charter school? I sympathized up to a point, but found most of what she hated familiar, but by turns sad, funny, and mostly harmless...she may be a zookeeper, I said, but I live in the jungle, and as such, have had to make peace with my environment, not fight it. She replied by hotly denying that I had any idea what she was talking about...it was inconceivable that anyone like me could live anywhere near what she had to deal with, much less know and understand its ways. Finally, in utter despair, I laughed and said, as tenderly as possible "Oh, don't be an uptight white bitch. Live a little. Be a sistah."
I was tossed out on my ear.