
I think it's worth it to leave at least a little space around your bamboo if just because the shoots sell well when they appear. I just make checking the bamboo part of my daily routine, like digging up fossils and hitting the money rock. It's a completely passive way to get extra bells.
That said, if you're not the sort of person that does the daily routine sort of thing, then yeah, it may be better in your case to block the bamboo in. You said you have it growing in front of the mayor's house, though, so if you're playing as the mayor, then you wouldn't have to go out of your way to check on it. Either way you have some different options to choose from.