however the best translations are rarely literal,
this doesn't mean that they can be grammatically incorrect though!
"zostań moj / moja" is totally incorrect. "zostań moim / moją" require an object.
"bądź mój / moja" seems gramatically correct and would probably sound OK in the right context.
If by "be mine" the OP means "marry me", then the obvious translation would be "wyjdź za mnie" or possibly "zostań moją żoną / moim mężem".