The bikini is beachwear that is designed to provide comfortable clothing for swimming and getting a tan, much in the same way as speedos for men. The only sexist thing about bikinis is that half of them is intended to cover the breasts, when women's nipples should not be considered any more obscene than men's nipples. It would be even less sexist if women only wore the underwear part.
The burqa was specifically designed to help keep women as chattel, serves no practical use, does not aid comfort, and so is not at all comparable.
Moreover, the very idea that women wanting to appear sexy is sexist is extraordinarily sexist in itself. A woman's sexuality does not simply exist for men, it exists for herself too, and if a woman is expressing her sexuality it's pretty sexist to assume that she must only be doing it for male pleasure. She may also be doing it for her own pleasure. She may even gain pleasure from the thought that men are looking at her.
It's shocking that women have been wearing bikinis since the 40s, and the sexual revolution happened fifty years ago, and you people still don't have a clue.