Please provide background: Where did this fragment come from?
Context: What is the subject of the text?
Full sample sentence: Fragments are easy to misinterpret; please give at least a complete sentence.
Feminists burnt their bras in the 1960's to show their refusal of all the constrictions of sexism. "Bra-burning feminists" is often used disparagingly to denote radical feminists, ones that refuse to submit to societal insistence upon exterior displays of femininity, such as bra-wearing. Some people see this as an attack on men for whom these exterior displays are supposedly intended, and thus "bra-burners" are misunderstood as "man haters". Since the desire to please others is historically seen as a feminine trait, the lack in a woman of that priority is sometimes labeled as "bitchy". You can see then how "burn-the-bra bitchiness" came about, and hopefully how insulting it is.
The origin of the bra-burning myth is the 1968 "Miss America" beauty contest in Atlantic City. Several feminist protestors crowned a sheep and threw high-heeled shoes, bras, curlers and tweezers into a bin. Although they wanted to burn their bras, they were advised by the police that it was too dangerous. The plan was mentioned in an article in the New York Post, the headline writer called the women "bra-burners" and newspapers and magazines across America ran the story without bothering to read the original article.
I agree with jusap, the expression "burn-the-bra bitchiness", whilst being a nice piece of alliteration, seems to be intentionally offensive.