Bruce likes Percy. He really doesn't understand him, uh, at all, because what is normal teenage behavior, but he relates to Annabeth enough that because he's important to her, Percy gets an automatic pass on Bruce's part. His easy-going friendliness in their one thread affirmed that, and Bruce really needs more of that in his life. LOL.

He basically doesn't know enough yet to have any deeper feelings. Like you said in yours, Percy is that kid that is attached at the hip to Annabeth and comes around the garden a lot and is helpful. He has vaguely positive feelings about him, and there's that lurking undercurrent of concern, which I already went into the origins of. o/