1. The buses from DTD don't go to parks and have long routes. You would have to use a Disney Resort as a transfer point. Expect 1.5-2 hours per direction between your hotel and park.
2. There are hotels within walking distance not owned by Disney. Palace Hotel, Hilton, Best Western, Double Tree, Clarion and a couple others, all on Lake Beauna Vista within a half mile of Downtown Disney. These have their own shuttles.
Beyond that the hotels get miles away. The place is huge.
There are hotels that have shuttle like those above. A problem is they aren't free.
So look further away and do the math. Is a value resort onsite cheaper, or a hotel off site plus rental car and parking.
Be Cool Stay in School!
Next year I'm trying for a summer internship at Stark Industries.
For the hotels on Hotel Plaza Blvd, I've stayed at the Hilton, Royal Plaza & Wyndham (back when it was called the Grosvenor). Those are all walking distance to DTD. But like it's been stated, the busses at DTD do not go to the parks. But the hotels on Hotel Plaza Blvd have their own busses that take you to the parks, but from what I know they're not as frequent as the busses for the official Disney hotels.
I usually stay at the Clarion Inn on Palm Parkway, which is about a mile from WDW property. It's clean, the rates are cheap and the hotel staff is friendly. This is a hotel I stay at multiple times a year. They have free shuttle service to some of the parks, but their schedule is pretty much, drop you off at the park at opening and pick you up again when the park closes (or before). I've never used them, so I don't know the exact schedule how they run.
I've also stayed at the Holiday Inn Express (which is also on Palm Parkway) and the Radisson on 535 next to the Crossroads (when it was a Days Inn). Both of those were nice as well.