As a general rule, one should allow at least 30-60 minutes to get anywhere on Disney transportation.
For MK to DD, it is recommended to take the monorail or ferry to the Transportation & Ticket Center, then get on a bus to Downtown Disney.
There are 3 stops at Downtown Disney.
1. Marketplace
2. Pleasure Island
3. West Side
From there, that bus usually makes another stop at Typhoon Lagoon (if open) before heading back to the TTC.