Have Hertz pick you up. I have rented from there. They came to CBR to pick me up. I returned with them, completed the paperwork, and then had the car. Returned the car to SOG and they drove me back to CBR and it worked out just fine. Tell them what time to pick you up and they will do that. No problem.
Yes, there are dedicated buses (owned by SoG, not Disney Transportation), but I believe you have to show a room key to get on those buses.
And, yes, non-military folks are allowed on the SoG property -- in fact, you can even shop at the AAFES General Store (Mini PX) for snacks/Disney souveniers -- the only exception is alcohol/tobacco (as they are tax-exempt, those items are sold to ID card holders, only).