The bus service only runs on weekdays. So on Saturday and Sunday you cannot get to the airport's railway station unless you take a taxi (£9 when I did it - you can't help but feel cheated when you get out of the taxi and see the aircraft you stepped out of moments before :x ).
At the weekends, you are much better to get the 727 to Aberdeen City Centre and connect with rail services there. I'd only waste money on the taxi if I was going towards Inverness, where the low service frequency means that you may face a considerably longer journey if you don't. All in all, the 727 bus is by far the best way to get between Aberdeen and its airport - when I lived there, using the train never crossed my mind.
Yes, it is a disgrace. That's Aberdeen for you. Bear in mind that the 727 bus is actually relatively new - it launched in 2010, and before then you were stuck with either an infrequent train or a horrendously overpriced taxi.