For day trips to the mainland, you probably do not want to try to rent a boat to take you back and forth, as that will cost a LOT, in money and possibly in hassle. I'd suggest either work your schedule out to fit the ferry (it's actually a glorified water taxi) or fly at least one way to/from the municipal airport, which is pretty cheap. Fares San Pedro<->Belize City are about half as much via municipal as via the international airport.
There are no buses at the international airport, or at muncipal. From municipal you'll probably want to take a short taxi ride (cab, that is) to whatever bus station you want.
Actually, it's probably easier and certainly will make it faster just to rent a car for the day rather than fool with buses, as to get to Ian Anderson's you'll have to change buses in Belmopan, plus the lodge is not directly on the road.
Overall, you might be even better off going over for the night, rather than trying to do it as a day trip.
Belize First magazine http://www.turq.com/belizefirst/