You would probably save time by leaving the bikes at the Rothiemurchus Lodge.
After rain the boggy bits up to join the Lairig track from the Lodge might require some dismounting and pushing....to get further on a bike would be a bit of a toil …...with .lots of stone culverts to navigate or maybe even hop over on the bike.
I have only been on the Lairig track on the descent. Much easier walking.
Have you considered cycling up to close to Loch Eanaich ….Cairn Toul with a bit of doubling back to take in Braeriach with a descent of ridge between Coires Lochan and Ruadh…..you will end up a wee bit below the bikes ...recover and enjoy the fast ride out.