DisneyQuest is at DownTown Disney, so unfortunately there is no direct bus service. If you are staying on site, you could go back to your resort, then transfer to a Downtown Disney bus/boat, other option include the ever popular car, or you could try exiting the Magic Kingdom, taking the resort monorail to the Contemporary, and catching a Downtown Disney bus from there.
When you get to Downtown Disney, if traveling by bus be sure to exit at the stop by Planet Hollywood, not the stop by the Rainforest Cafe. If driving park in the Westside lot.
If you ride the boat to Downtown Disney, if you are there at 4pm or after you can trasnfer to the West Side boat, if not you can either walk it, or see if one of the bus drivers will take you to the other side.
How much time you need depends on the crowds and you. I went after the parks one night and got about 80 minutes as DisneyQuest and hit all my must dos, but I did not have the luxury of time to really explore the place.
(My must do's were Cyperspace Mountain, Mighty Ducks Pinball Slam, and the Buzz Lightyear Astro Blasters), I also found time for Alladi's Magic Carpets, and the Virtual Pirates of the Caribean.
I did however, have the luxury of having available plus options so I did not feel like I just wasted a whole day for that hour and a half.
