Another vote for offsite rental. That way you can use it around the resort also
100% agree. Both my husband and I, on separate occasions, had to use a wheelchair while at Disney World and only for that trip (the stories would take pages to explain). We rented from offsite each time and with my husband's visit, we stayed offsite. Each time, the pick up and drop off were so very easy and it really helped for each and every minute around the resort/hotel and getting to and from our transportation to the parks and back again.
Just so you know, the offsite place will deliver the scooter to your resort on the day you are arriving. You pick it up at the front desk. When you leave, you drop off the scooter at the front desk. And the cost is very reasonable.
As to your original question, take the bus from the All Star to Magic Kingdom. He will have his scooter with him and will be the last one off the bus so he can take him time and then wheel himself to the front entrance.