The context is F. Scott Fitzgerald’s “Bernice Bobs her Hair.”
Oh, I wasn’t thinking about that. I was considering whether we
hadn’t better bob your hair.
Later on in the story, we are clarified that Bernice’s hair isn’t the Bob cut when Marjorie offers this advice. So the situation is that Bernice doesn’t have her hair Bob cut, but Marjorie is evaluating the prospect of her getting said cut. To me, it seems like the correct modal phrase to use is “had better,” but “had better not” is used, implying that she already has a Bob cut when Marjorie is talking to her (and before her subsequent fainting spell).
What is Fitzgerald saying?
It’s an old-fashioned usage. In the scope of phrases like wonder if, or don’t know whether, the embedded question is made negative where today people would make it positive. The purpose seems to be to make it more tentative, and hence more polite.
A couple of examples, from searching for “wonder if you can’t” in the Corpus of Historical American English:
From A Fearful Responsibility and Other Stories, by William Howells Dean, 1881: ‘”I wonder if you can’t help us,” said the consul.’
From Mother Carey’s Chickens, by Rachel Crothers, 1917: “I wonder if you can’t make it convince your father?”
In both of these cases, the request is clearly positive in intent (they want help, or convincing the father), but it is expressed as a negative.
Here’s one as recently as 1982:
From Manseed, by Jack Williamson: “I wonder if I couldn’t get in touch?”.
Out of context it would be possible that this means “I wonder what would happen if I couldn’t get in touch”; but the reply is “Don’t! Don’t try that?”, which makes it pretty clear that this is a suggestion, and the meaning is positive, not negative.