Theroz,
I did understand you about the airport shuttle bus -- which I think is run by the airport authority and not the hotel -- at least I had read that somewhere. I seem to also have read somewhere that some family of 4 had complained that it was the last stop on going to the airport and that at the time they caught it, it was very crowded for them. I just hope that it will not be raining when I go to the airport -- of for that matter, when I am in Edinburgh!!
Unless I do misunderstand you, you plan on taking the bus to/from the airport to the city center and back again.
I just wanted to point out that I had read somewhere that taking the tram from the city (wherever that is) will leave you possibly closer to the D/T Edi than does the express bus from the city.
Since TBS seems to have this down pat, I defer to him/her as to whether the things that I had read -- but have not researched in detail as I do not plan on staying at the airport D/T -- are accurate.
In any event, I would like to wish you and TBS a big thank you for your contributions and wish you a wonderful time in Edinburgh!