I don't think there is anything that goes straight between them. Everything I've found uses Pheonix as a hub so you'd have to go back to Pheonix (or at least towards it) and then back out. If you catch the commuted bus to Cottonwood can you get anything from there to Flagstaff?
How much luggage will you have? It's only 30 miles. I would consider walking. You might be able to get a taxi but that could be expensive. I guess that leaves hitchhiking.
Try contacting their visitor info centre at
info@sedonachamber.com to see if they have any suggestions.