A person - who could be of either gender, but stereotypically is a woman - who allows their spur-of-the-moment negative emotional reactions to play far too large a role in their dealings with others.
The most recognizable characteristic of a bitch is a high volume of largely unmerited complaints about others. To qualify for bitchhood, these must be a conspicuously frequent feature of her conversation, and must strike most non-bitches as exaggerated if not completely unwarranted, at least occasionally to the point of making a big deal of things that strike most others as completely innocuous.
Note that a frank but perceptive critic of others is not thereby a bitch, even if completely lacking an internal censor. Bitches frequently think of themselves as such people, but in reality they have the frankness, but not the perceptiveness.
The bitch will often come across abrasive and unreasonable, except to authority figures who can benefit her. Most are narcissistic and/or hypocritical; favourite tactics include characterizing things as horrible moral wrongs which are unobjectionable save that they inconvenience him or her personally, and complaining that someone else has been rude to them, in terms that are vastly more rude than anything the complainee has actually done.
This is not the worst thing you can call someone, but it's about the worst thing I would call anyone I might nevertheless be willing to voluntarily spend time around.
One of our friends is homeless at the moment, so we were going to let him do volunteer work instead of paying for the convention, but this one bitch complained that it was somehow unfair that she had to pay and he didn't.
When I mentioned my money problems, she just insinuated that they were my own fault, but when her parents threatened to cut her allowance the bitch wouldn't stop whining about it. She'd still have had more money than me, too.