The AMC is expanding the number of stops on there daily shuttles arround the whites. Here is a link
The shuttles are oriented to support the hut to hut hikers so the timing may not match the immediate needs of AT section hikers but it is an option with a bit of planning. They are also useful in case of a "bail out" situation as they run daily and typically have room. The link also has links to other public transportation options to get to the white mountains.