Okay, come on now. There's gratuitous, and then there's cheesecake, and then there's this.
After Kara/Lobo (and just before Ollie/Deadman) Jaime/Batman was my favourite teamup from Brave and the Bold. Their personalities are completely different: Batman is dark and broody, while Jaime is fun and happy. He really wants to impress Batman, and Bats is just trying to help him be a better superhero.
Where Batman really shines, in any comic that he appears, is when he's trying to teach/help other superheroes. You would think that since Superman is nice and pure that he would be the one to mentor others, but he really isn't. He has the "Super Family" but this mostly consists of people tangentially related to him (Peej being his otherdimensional counterpart's cousin, Kon being his partial clone) who go off and do their own thing. He doesn't even hang out with Krypto that much. Bats actually mentors and teaches all of his sidekicks (by my count: three Batgirls and five Robins) and is involved in their lives and continues to be involved after they evolve (ex: Oracle, Nightwing). Not only that, but as I said before, he often supports the heroes who don't receive much support elsewhere (Booster Gold, Plastic Man). I'm not a huge fan of his mostly because I prefer my comics to be both funny and optimistic in tone, but I really like him for that.
Jarvis is no Alfred, who can extricate himself from virtually every kidnapping situation, but he tries.