You have several options.
1st, you can take the Doubletree bus to the TTC, then transfer to a SOG bus. If the driver asks, just show your ID and tell them you are buy tickets. In my one time riding the SOG bus, he didn't ask.
2nd, you can take the Doubletree bus to the TTC, then walk (head towards the Polynesian, then find the crosswalk and the pathway to SOG)
3rd, you can take the Doubletree bus to the TTC, then take the monorail to the Poly, then find the crosswalk and walk to SOG
4th, you can walk across the street to the Disney DTD bus stops and take a bus to the Poly, then find the crosswalk and walk to SOG.
Hope this helps.