Private cars can't go into the park past canyon junction, unless you are staying at the Lodge. Buses run very frequently, so definitely recommend taking the shuttle in.
There's limited parking and restricted access for personally owned vehicles in the park. I would definitely opt for the bus from Springdale myself. It's free and you'll get to all the trails easily.
The park has free buses going right up to the park. Many places to get on a bus, so I would take the buses if staying in Springdale. Also the park has buses to take people to the hiking trails.
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