I recently went from MK to Typhoon Lagoon on a Saturday around noon. Took the monorail to the TTC, and the bus from there. It took a while. We were lucky, and got a bus at the TTC almost immediately. However, the bus makes 3 stops in Downtown Disney before going to Typhoon Lagoon.
I suspect that all Disney buses do the Downtown Disney stops before Typhoon Lagoon. That was the case for the bus directly from the Port Orleans resort also. So ... it might not be any better to catch a bus from a monorail hotel than from the TTC.
If I were doing it again, I would consider taking the monorail to the nearest resort (Contemporary) and taking a taxi from there. I bet that would have saved close to half an hour of time for $10-$15.