I purchased a Hampton Bay ceiling fan with 4 lights. I just noticed the bulb base is smaller in size. Can someone tell me what size the screw-in portion of the bulb is so I can purchase them online?

I believe the base you have is call Intermediate with a code of E17, smaller than the standard medium, and larger than candelabra bases.

Plenty of fans now have candelabra bases too, so it could be that as well.