If six people work on a job and they all do the same amount of work to get the job finished, then they have all done their fair share of the job. If you and I were dividing something that was given to both of us and you got twice as much as I did, then you would have more than your fair share and I would have less than my fair share. A "share" is a portion of something and a "fair share" is a portion that is fair, honest and right. In the sentence, "When we were partners,we busted our fair share of hideouts.", it appears that these two people were partners, possibly police officers, and that they discovered the number of hideouts (maybe criminal hideouts) that would have been expected of them. In this type of statement, it could mean that they busted at least as many as they should have and possibly more.

Getting your fair share= getting your "equal" piece of a meal, a business deal, or any other transaction. Fair means even-handed, and appears as an adjective. Share is in this case a noun, also expressed by talking about someone's "cut" of something. If there was a chocolate case with 6 pieces and there are 5 people who will eat it, everyone will get their fair share which is one piece of chocolate cake.