Sure Graham - easier to show you on a map. Where do you commute from & what time?
This is my default route at the moment whilst the Metrolink is being put on Mauldeth Rd-normally I would go up Mauldeth Rd, then up Withington Rd or Alexandra Rd South.
The key to the route is to go through Sale Water Park and pass Jackson's boat pub as this gets you into Chorlton. From there you have a multitude of routes to take. The path to Hardy Lane is fine for road bikes too.
On the route I have posted, instead of heading to the big roundabout just outside Deansgate on the A56, there's a shared use pedestrian bridge that takes you over the Mancunian way.
[edit-just noticed that the route turns right in Chorlton on Wilbraham Rd and left onto Withington Rd. I wouldn't normally take that way, but just continue on Manchester Rd, then take the right fork onto Upper Chorlton Rd).