We were in Zion last week. For the portion of the road that goes up towards the lodge/narrows/angel's landing, you can either take a shuttle or you can park at the visitor center and walk/bike up. Shuttle tickets are released in two groups, months ahead of time and again at 5PM the day before. You have to reserve your preferred hour between 7AM and 2PM, and each hour window has ~350 tickets. We were very careful to have the reservation webpage preloaded and on-screen right at 5, as we'd been warned tickets sell quickly. The 8AM slot was gone within 5-10 minutes.
We were able to get our preferred 8AM slot, and we showed up in line right on time. There are a couple benefits to the limit, namely that the shuttle line is virtually non-existent early in the day and that the valley is, for the most part, not crowded. Moving between stops inside the valley required almost no waiting if you do it by shuttle. I did hike to angel's landing around 9:30 or 10 and by then there were enough people even with the ticketing that it was very crowded, but other hikes that day were more sparse.
Lane Hog, if it's helpful, you don't have to arrive at the top of your hour. You can get in line/on the bus over the hour-long range.