I've not cycled the north side of the loch, but I did walk down Coire Leachavie from Mam Sodhail a few years ago and the track was very loose with fairly big rocks and quite eroded, so for me it wouldn't be worth the bother of cycling it.
However, another option for you would be to cycle on the south side road which is a good ride, then go up from there. See my 2013 trip report:
https://www.walkhighlands.co.uk/Forum/viewtopic.php?f=9&t=32549. You could do a variation of this, leaving your bike at the point where we ascended and then walking down Coire Leachavie on the descent.
From memory, apart from the initial grassy slog up to the ridge, it was a great day out. While you'd have a longer cycle it might be more enjoyable ...
Have a good day, anyway!