A fuzzy mouse for a BP is way small.
I would say a regular feeding schedule right away is important. Otherwise you face a lot of general confusion and wasted food items (are you sure he's hungry? Sometimes they just like to explore, and pitching a mouse/rat to find that out is fairly unpleasant). I would also like to point out that snakes are generally opportunistic feeders, and just because they will eat when offered food does not mean they are as hungry as you think. Feed appropriate sized prey items (how big is your python? How big is the food you're offering?) at a proper pace (3-5 days for hatchlings, 5-7 for juveniles, 7-10 for adults).