First, I would never take anything unregulated like Uber or Lyft. I simply don't trust getting in a car with whomever.
Second, the solution for people who hate transit is to stay in the Epcot resort area, which is in walking distance of two parks. Epcot has the monorail system, which links to Magic Kingdom. Unless you're going to Animal Kingdom, a water park, Disney Springs, or some other area, you can avoid buses and other modes of transit altogether.