From the bienvenue website
"Indeed, bicycles are authorised on the green path - on the wooden planking west of the walkway (measures ensuing from the municipal decree of the town of Mont-Saint-Michel dated 01/12/2014):
from 1 October to 30 April, 24 hours a day.
from 1 May to 30 September, before 10am and after 6pm.
Parking your bicycles is strictly prohibited all along the dyke walkway, the esplanade and at the foot of the fortification. Cyclists are thus required to leave their bicycles in the designated areas and to pursue their trip towards the town on foot or using the shuttles."
I had heard this via word of mouth as well - so early or late and no stopping should be fine.
HTH
Julia