The DTD shuttle buses run pretty good on schedule. Right now :25 and :55 past the hour. And run till 90 minutes after park closings.
You are going from the Hilton LBV and that is the 'A' Bus route and you will be first to be picked up and dropped off. Having said that, your trip will be longer to the parks as you are the first picked up. The 'A' Bus route goes:
Hilton LBV
Holiday Inn
B Resort
Double Tree
I timed the trip from the Buena Vista Palace to Magic once and it was under 20 minutes. Now that was the last resort pick up so you can add maybe 5-10 minutes to that ride time from say the first resort pick up, which you would be. Barring any assisted loadings needed for people in ECV or wheelchairs.
I would think from the Hilton LBV to EPCOT should be no more than 20 minutes or so. As I said, they do run pretty good on schedule and it will be your best bet to get to the parks from DTD resort area hotels on those shuttles.
Here's a hint as well. On your way back, you can get on the 'B' Bus from the parks and get off at the Wyndham LBV right across the street if the 'A' Bus to your hotel is not the first bus to get to that park you are at and just walk to the Hilton. We do this all the time at DTD hotels.