Why does Audrey Hepburn's character ask for 50 dollars from her admirers every time she goes to "the powder room"?

Holly was simply fleecing the men for their cash, ostensibly to pay the toilet-room attendant but in reality she was pocketing the money and using it to pay her rent and living expenses

In the source novella we get this exchange;

"I wasn't impressed by the honorarium either; you can do as well as that on tips to the powder room: any gent with the slightest chic will give you fifty for the girl's john, and I always ask for cab fare too; that's another fifty.".

Note that Holly isn't a prostitute (she rarely sleeps with her dates) so much as a semi-professional "good time girl", making the men pay for her company under the pretence of being on a real date.

Truman Capote spoke about Holly in a Playboy article from 1968

Playboy: Would you elaborate on your comment that Holly was the prototype of today's liberated female and representative of a "whole breed of girls who live off men but are not prostitutes. They're our version of the geisha girl..."?

Capote: Holly Golightly was not precisely a call girl. She had no job, but accompanied expense-account men to the best restaurants and night clubs, with the understanding that her escort was obligated to give her some sort of gift, perhaps jewelry or a check ... if she felt like it, she might take her escort home for the night. So these girls are the authentic American geishas, and they're much more prevalent now than in 1943 or 1944, which was Holly's era

It's been a number of years since I last watched this, but I think it was something like this:

Holly Golightly is an aspirational character (i.e. she is trying to appear more than she is). At that time, rest rooms were largely staffed (in good restaurants/tiffanys etc), and as part of using it someone like Holly would be expected to leave a tip.

Being poor, Holly would "borrow" a $50 bill from her date (a largish sum at that point), then when leaving she would be able to say to the attendant "Sorry, that's all I have", avoiding paying the tip, without looking cheap (and keeping up the image of being well off). You can draw your own conclusions about what happened to the $50 afterwards.

It's kind of like Chris Elliott character in Groundhog Day in which he pretends to leave a big tip to impress or appease his lady friend (want-to-be-date) only to keep the money as she's turned her head, walking away. In fact, many if not most of the men are looked down to as pathetic characters who we laugh at including the star, Bill Murray, who we 'all' love and adore. No wonder we find ourselves in a most challenging situation in this country including politics where American woman want to be rich, socially respected, dominate over others and in control of their lives and others. But that's not politically correct to say or even to understand, just like Audrey Hepburn's character in Breakfast at Tiffany's. We like living a lie to others and ourselves especially in a heavily religious infused country, and the book story gets watered down in this country but probably not elsewhere.