20-30 minutes sounds correct. You could try to leave your room at 07:30am sharp, and someone won't be ready, so you'll be waiting around for 10 minutes. Or you could walk down to the hotel lobby, and then realize you forgot something and have to go back.
So trying to leave at 07:30am is a good idea in case there are delays. If you get to the gate at 08:00am, that's good, a line will already be forming, and you want to be near the front. In August, the parks usually open early.
It is a long walk, probably about a mile from the BW to the gate. There are moving sidewalks once you get to the 3rd floor of the parking garage.
Going back to your room in the afternoon is a great idea. Eat lunch, rest, and then come back in the afternoon at 6pm when you can park for free.
Everything will turn out great, just get that early start and take a lap of walk on rides each morning. Around noon, it will be very hot, lines long, and you'll know when it's time to leave. After 4-5 hours of non stop walking, my feet get tired, and I need a rest.