Assuming you start from the Notom Bullfrog Road and park just off to the side. Hiking up-stream the narrows start I'd say less than a mile from the road. It isn't a real slot canyon per say but it does have some photogenic narrows. There was only one or two spots where you need to hoist yourself up a boulder or two otherwise it's a very easy walk through.
This canyon is actually very long so you can make 4 good hours by hiking up for 2 and then turning around. You'll see the best parts after a couple hours anyway. Have fun out there.