The shuttle bus system is the main transportation system for denali np, The single road is 95 miles long and private vehicles are not permitted in order to preserve natural habitat and ecosystem. The bus schedules and how the system works is on denali's website. You can get off of the bus and hike and later flag down another bus along the road. In the heart of summer late June-late Aug, it can get crowded on the shuttle buses and you may have to wait for a seat. They can be reserved in advance and you should do so. Buses run throughout the day as the sched shows. The buses stop at several rest stops along the way, about every two hrs, plus stops for wildlife, but for those you cannot get off. The stop at Eielson Ctr or Fish Creek (for 2005 season) will be for a little longer and you have time to walk around and still get on your bus. If you go all the way to Wonder Lake and back, about 12 hrs, you will have about 1/2 hr at the lake.
The longest stop will be at the destination, at most 45 minutes. The other stops are brief bathroom stops- about every 1/2 hour. You can get on ANY shuttle bus that has seats if you wish to hike, buses are frequently going by. Just step up to the road and flag down a bus, they will either pick you up or tell you when the next bus with seats will be coming by. IF an area looks of interest to you, you can just ask the driver to stop and if in a safe area they will drop you off.