We did this a couple of years ago. It was very easy. From Downtown Disney (parking lot near Cirque De Soleil) take the #50 bus. The fare back then was $1.75 each way. Ask the driver to tell you when to get off for SW and where to pick up the return bus (also #50). For schedules and further details, www.golynx.com.
Buses from the resorts to DTD usually start around 8:30 a.m.
If you want to leave earlier, and don't want to drive or take a taxi to DTD, the Lynx bus also stops at TTC. You should be able to get a bus from your resort to MK around 6:30-6:45. The monorail from MK to TTC starts at 7 a.m.
Let the driver of the bus to MK know that you are going to TTC. He might be able to drop you there, especially if you are the only ones on the bus.