Park in Springdale and take the Springdale shuttle to the Zion entrance then walk over the bridge and catch the Zion shuttles. You will stay on until the last stop, the Narrows.
They don't allow cars in the park. The shuttle is awesome. Our guy was quite entertaining. The shuttle will bring you pretty close to the start of the trail that gets you there.
we were not there but if the shuttle still operates i suggest to use it. and sleep at springdale.
Depends where you enter from, but plan on finding parking asap, then wait for shuttle.
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