Indeed the airport bus is a very good option. If you are staying overnight, the HI on Glasgow Road next to the zoo is right next to a airport bus stop, as is Haymarket Station.

If you can get yourself to Queen Street station (bus?) by 0600, the train gets into Haymarket at about 0645 from where the airport bus or taxi (£12) will get you out to the airport by 0715 latest. The next connection is 0630 getting you to the airport by 0755. Sunday mornings night be trickier.

Traveline Scotland, on 0870 608 2 608, is very good in my experience. And the staff are actually based in Scotland...beats having to ask someone in India for trains between Kyle of Lochalsh and Achnashellach