Both are correct, but the first could mean you don't like apples and bananas together, but to make that clear, you should say I don't like apples and bananas together. There really isn't a rule about using and in a negative sentence.

In English, "or" is used in negative sentences to join one or two nouns, pronouns, adverbs, verbs, dependent clauses, and so forth. Negative sentences include the use of adverbs like not or never. Hint: if not is used once, it is most likely that "or" will be needed. For example, I don't like apples or bananas. Second example, English isn't quick or easy to learn. Hint: think of the full conjunction pairs of (both... and), and (either...or). For example, She likes (both) apples and bananas. She doesn't like (either) apples or bananas. (We would never say: She doesn't like either apples and bananas). In English, "and" is used in negative sentences to join two independent clauses. Hint: if "not" is used twice, then "and" will most likely be needed. For example, I don't like baseball and I don't like volleyball, either. These sentences are possible but longer. Native speakers often prefer the shorter versions with "or." For example, I don't like basketball or volleyball.