What should I do about this gap between the tub and tile?
OK this is a lot of talk about a very minor issue.

First the issue is because you laid your first row too high (or it's slightly off level).  I would also suggest going a little further out of the tub but if your tiles laid out to that width without cut I could see stopping.  

Grout the gap.  Anything else would be silly at the point.  Also your grout color matches your tile well so should not be an issue.