OK, a lot of this really depends on your time of travel and aversion to cycling in traffic (if at all bothered?). The route suggested by ColinJ is a possibility but with a little local knowledge I would tweak it to
THIS if you want to use the Fallowfield Loop. Once you cut out the crap around Ashton and tidy up the zig-zag bit from the Fallowfield Loop out to the airport it is actually a pretty good route.
Probably my preferred option would be
THIS as it possibly uses the quickest cycling roads to keep the journey time to a minimum (quite important if you are doing this regularly?). As it happens it follows a good chunk of my commute as I ride Ashton to Hazel Grove.
I would avoid Cheetham Hill road like the plague! It is busy, double parked and cars go too fast for the confined space it creates. The roads I have chosen are more open and spacious, although you will never escape the fact this will be a largely urban commute.
If you ever want to practice riding any of the routes give me a shout and I'll see what I can do. A new cycle buddy in the locality won't be a bad thing
