Considering the fact that Batman goes days without sleep, I'd say he doesn't take the time to take a quick shower either. So yeah, he probably does smell most of the time. He most likely takes showers, however, when he finds the time to sleep. So, that's most likely every few days.
It's interesting that a hero/villain performs one amazing feat, or use a power they haven't used for 20+ years, and that automatically propels them to a high status despite scans and evidence to the contrary. I don't know what is worse, selective feat picking that has only been done once or twice 20, or more, years ago or ignoring evidence from scans or the lack thereof. We need to stop putting our favorite heroes/villains on pedestals and start putting them where they really belong. But it's evident that people never will because they would rather accuse others of cherry picking feats, when they don't, and being 'morally superior' when they aren't. I guess being honest and as fair as possible only opens one up to being the target of childish accusations and fault finding by those who insist on acting petty and childish. What happened to a good debate between two civil, mature, adults?