I'm not sure what the rules are about media references here, but haveHave you watched FireflyFirefly? Malcolm Reynolds and Simon Tam have a relationship that could be a good inspiration for your character.
Mal thinks Simon is ridiculous. He puts the entire ship at risk just by being there, his sister is unpredictable at best... sure, he's a great doctor, but for the most part he makes living on the wrong side of the law much harder. Nonetheless, when push comes to shove, he has Simon's back. Why? Because Simon is part of his crew, and he's loyal to his crew.
Your characters have probably been through a lot together. "Alice finds Bob ridiculous, but they go through some stuff together and form a strong bond, even if they never really find a common purpose" is a tried and true storytelling technique.