Student or Learner
how often does this bus pass by here a day?
how often does this bus drive by here a day?
which one is more appropriate, please?
I would probably just ask, "How often does the bus stop here each day?" If you say "drive by" or "pass by," it implies that the bus doesn't stop.
If the bus actually doesn't stop, and you just want to find out how many times during the day the bus goes by, then your sentences are about what I would use. Either "pass by" or "drive by" would be fine in this case. It wouldn't matter.
Not a teacher, but this is how I would speak it.