Like everything, it all depends on context. Bitch isn't universally sexist, but if it's said in reaction a reasonable action where a woman is asserting herself, it can be sexist. And it's almost universally sexist to refer negatively to a male as a bitch as it implies a lowering of stature through femininity.
For what it's worth, I don't believe that's the case here and I'm fine with people calling her a bitch, though I wouldn't do so myself and can see how others would find it inappropriate. She comes off as someone with a huge axe to grind and looking for even the slightest of provocations to push her agenda. She overreacted and deserves most of the blowback she's getting. Of all the behavior of everyone involved, hers is the only one I find malicious and reprehensible. The rest just showed bad judgment and/or were put in a no-win situation (read: the employers.)
The saddest part about this whole incident, to me, is how everyone is conflating 'sexual' with 'sexist'. From everything I've seen on the comments they were sexual, probably not safe for a work environment, but I don't see them as being sexist unless you buy into the puritanical, anti-sex agenda that tries to convince women that they can't enjoy sex as much as men. The undercurrent of this whole brouhaha is the culture that seeks to repress women and make them believe that they'll be branded 'sluts' or some other derogatory term if they actively pursue their sexual desires. Otherwise, why would they need to be protected from dirty-but-non-malicious jokes like the one in question? If the result of this incident is that women are over-protected, coddled or treated with "kid gloves" in the tech work environment, then we've all--women most of all--lost as a result.