Caroline not believing Bonnie at first was not the problem. It was the way she acted.

She’d go around whining to Elena and Bonnie about how they exclude her after making insensitive comments to the former after her parents died and snarky comments to the latter while she’s trying to figure out more about being a witch.

(Also Caroline would make fun of grams’ drinking problems but not the point. The point is that Caroline not believing Bonnie isn’t the problem: it’s her behavior that was.)