Some of the discussions and panel presentations as of late have brought up the idea that Brett embodies the image of "The New Woman". I think this is true, to some extent. Brett's heavy drinking, smoking, short hair and androgynous clothing suggest that she tries to distance herself from traditional feminine stereotypes. It also seems that all the men in the novel are constantly vying for Brett's attention.
But I believe that Brett, in the end, is as dependent on men as they seem to be dependent on her. Brett relies on them both financially and socially. One example is after her break up with Romero, where she sends a distressing telegram to Jake that says she is trouble. She later confesses that she has run out of money. Is it possible that Brett sent for Jake mainly so he could bail her out of Madrid? On one hand, it's kind of sad to think about, but I think it's plausible.
In addition, Brett has never truly been alone throughout the course of the book. She was always with the Count, Cohn, Jake, Mike or Romero. It's possible that Brett needed these men in her life partially for financial support, but also partially to exert her dominance. We see Brett toy with the emotions of the men throughout the novel. We could debate about whether or not it's intentional, but in the end, her flirtatious manner is a huge part of Brett's character either way. It's a very 'Brett' thing to do.
Because Brett is so used to interacting with men in that certain manner, it's odd that Brett is so emotional after her break up with Romero. When she leaves Mike for Romero, Brett doesn't think twice about Mike. But as Brett tells her breakup story to Jake, she is visibly shaken and lacks her usual self control. She tells Jake that they should stop talking about Romero, but Brett herself keeps mentioning his age, birthday, and language skills, among other things. In addition, Brett says that Romero was "ashamed of [her] for a while", but eventually got over it. However, a few lines later, Brett undermines herself by mentioning that Romero "would have gotten used to" her appearance later. The word "would" suggests that Romero was still disapproving of Brett towards the end of their relationship. These details seem to suggest Romero broke up with Brett, instead of the other way around.
This brings me back to Brett's need to asset her dominance over men. When Romero takes the position of power in the relationship, Brett is completely shaken. I highly doubt any man would have broken up with her before Romero (possibly) did, so rejection is a foreign feeling to Brett. In the end, Brett seems to realize that she cannot function alone. Thus, she immediately calls Jake to provide her with financial and emotional support, displaying how much Brett relies on the men in her life.