As Brian mentioned, the hotel hasn't opened yet, so we don't have a lot of details currently.
The Existing Time Share runs a scheduled shuttle to the parks. It is assumed that the Hotel guests will also be able to utilize this service. There is however some question on if the addition of a regular payed hotel may end up resulting in an increase of the shuttle service into a more regular "every 20min' sorta deal vs. the current schedule that tends to have a break in the afternoon.
For Timeshare guests there, often the preference is to have a car because of the additional freedom and the fact that the existing shuttle service does have some quirks (like the afternoon slowdown). If however you are someone who is planning on being out of the place first thing in the morning and not returning to the hotel/resort until late in the evening, It could be doable. Once you are dropped off at one of the parks or DTD, you can always utilize the Disney Transportation to get around the Disney Resort.
The Bonnett Creek resort area also isn't too far away from DTD or the Boardwalk areas, so if you do enjoy a late night out after the shuttle is no longer running or convenient, a taxi from DTD/Boardwalk shouldn't be too expensive and it may still end up ultimately less expensive than renting a car or staying onsite.