The context of the story is that he keeps buying drinks for women who flirt with him at nightclubs (e.g. one or another traveling singer) who then near the end of the night make some excuse why they can’t spend more time with him and leave.
He notices one of the women who made some excuse about a party that night has been talking with the MC frequently, and surmises correctly that they are married – turns out the woman wasn’t actually looking for romance and was just leading Feynman on to get free drinks out of him. The permanent singer at the club had been introducing women to him after first telling the women he was a big spender.
Feynman befriends the couple (singer and MC), and they talk about how plenty of rich men at the bar keep spending money on the girls there without getting anywhere romantically. The MC tries to teach Feynman about the social roles people take on at a bar. The key lesson is that a man who buys a woman a drink up front is unlikely to end up getting the one night stand he wants, but if he refuses to buy her anything, his chances will be better. Feynman tried it out by getting a girl to pay him back for a sandwich, and a few hours later she came by at the end of the night and invited him to her room, so the lesson apparently worked.
The “bitches” part is some kind of temporary psychological reprogramming he’s doing on himself for a day or two so that he can bring himself to objectify people against his usual inclination, so that he can try the experiment. It’s clear in context that he doesn’t think all women are “bitches”.
Feynman tried it one more time some while later on someone who wasn’t a traveling singer, flirting a bit with a girl but then asking if she would sleep with him before he would buy her a drink. She agreed.
His conclusion at the end is: “So it worked even with an ordinary girl! But no matter how effective the lesson was, I never really used it after that. I didn’t enjoy doing it that way. But it was interesting to know that things worked much differently from how I was brought up.”
Note: I’m not making any value judgments here, just recounting the story.