Can two bases be scored in one turn?
According to page 6 of the rules, the last thing you do after scoring a base (after discarding minions, and moving the First Mate and its ilk) is to "Check to see if another base is ready to be scored. Score it too, the same way."

So every time you score a base, you check all of the other bases and see if they're ready to be scored. The player whose turn it is still decides what order to score them in.