I realize that you want to go cheap! Lynx would cost you $1.00 per person PLUS .10 per transfer to take you to the Ticket and Transportation Center. You'd then have to catch Disney bus to ASSp. Honestly, it would be far more reasonable to pay $27.00 round trip for Mears. They will pick you up at the airport, and take you to your resort. It may not be as convenient as TTC or yourride, but it will work. The public bus would work if you don't mind a long trip and getting your luggage to the TTC for your trip back to the airport.
As adventurest as I am, I wouldn't go that route.
Gerri