Connectivity between Maybury and the airport junction is rubbish.
One option (a little indirect, and completely unsignposted for anyone unfamiliar with the area (like, I dunno, bike tourists going to/from the airport), but at least you can keep moving/cycling and don't have to try to struggle across the very human-unfriendly Gogar roundabout) for going west would be:
Go onto the footway at the (former) Comet entrance/exit (I think it has drop kerbs, it certainly should), or even at the Marriott Hotel, go beyond the Edinburgh Gateway underpass and then hairpin down the ramp to go through the underpass to the station;
Cycle through the station plaza, carefully ignoring the "no cycling" signs and that they built it a little too crampedly for comfortable shared use (an opportunity badly missed);
Cycle out of the station not-car-park;
Use the fairly mediocre "cycleway" footway along the north side of the A8 until you get to Gogarburn;
Spiral round over the Gogarburn bridge, and then take the dreadful insta-180° hairpin (seriously, who let that bit of golden rule 2 through planning) to rejoin the south side cycleway.
What should have happened when the tramline was being designed was that a parallel cycleway should have been built alongside it from Edinburgh Gateway (I know that came later, but it was in the planning at the same time) right up to the airport. But that would have been too much like common sense, I guess.