It is important to read this last line in the context of the rest of this short story, or exmaple of dialogue. Let us remember that the vast majority of this text are the words of the mother to her daughter as she offers her a series of snippets of advice about how to be a daughter and then a wife and the various jobs that these positions involve. What is interesting about this dialogue, however, is the way that the mother again and again returns to sex and accuses her daughter, perhaps unfairly, but certainly very harshly, about the way that she appears to be courting sexual activities in a way that is unbecoming. Note how the mother makes reference to "the slut you are so bent on becoming."

It is this suspicion that the mother has that leads to her wilful misinterpreation of the innocent question that her daughter asks her. Note the last few lines of this story and what leads to the final line that you are asking about:

...always squeeze bread to make sure it's fresh; but what if the baker won't let me feel the bread?; you mean to say that after all you are really going to be the kind of woman who the baker won't let near the bread?

The section in italics indicates the voice of the daughter, who is asking a perfectly innocent question. It is the anger and the suspicion of the mother that causes her to misconstrue this remark as being yet another indication of the way that her daughter is determined to become a slut. The last line then says a lot about the nature of the relationship between the daughter and the girl and the suspicions and fears that the mother has of her daughter becoming a "sluttish" figure.

What does "the baker won't let near the bread" mean in "Girl"?

All the way through "Girl" the mother alternates between giving straightforward advice and delivering lines that to an outside might sound close to abuse. The listening girl protests against the latter comments. The lines you asked about were said after one of the girl's protests, and they sort of sum things up. A woman who the baker lets near the bread is one that he trusts, so the mother finishes her speech by essentially topping her daughter's last protest and saying, "You mean you won't be a woman he trusts?" (You won't be a woman who is and appears good?)