When I was there about six weeks ago they were not letting people drive up the canyon. You need to take a shuttle, and have two tickets to go up and then come back.
You can. You'll be missing A LOT of the park by doing so.
If you decide to rent a bike you can also use a bike but if you look up "Zion Shuttle Tickets" they are $1 and go one sale at 9 am mountain time the day before you need them. If you plan with time, you can get the tickets 2 weeks or a month ahead of time too.
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