I've been looking into this as well, and it appears that the nearest bus stop is about a mile away, near the resort complex gate. "The Bus" website has a map showing the location and as best I could determine the trip into Honolulu takes about 1 1/2 to 2 hours (I've driven it in 45 min by car mid-day), depending on where you're actually going, with at least one change of bus. Good news is that the fare is only $2.50.
I also saw something about Aulani providing a bus into Honolulu 3 times a week for about $30 RT.
I'd also appreciate any additional information as we'll only be at Aulani for a few days before heading to Kauai. We visited Oahu last year so DW wants to spend our limited time at Aulani without a rental car.