If you’re visiting during peak season, which is from mid-May to mid-October, you will only be able to access the main site via shuttle.
The shuttle, however, only runs from 9:00-15:00. So if you depart early enough and get to the site before 9:00, it’s perfectly fine to drive all the way to the Visitor Center in your own car.
Whichever option you choose, from central Santa Fe, first head north along US-84 W. Eventually, you’ll turn left onto Highway 502 and then another left to head south along Highway 4.
If you’re visiting after 9:00, it’s along Highway 4 that you’ll find the White Rock Visitor Center which serves as the shuttle departure point. There will be big signs so you can’t miss it. The shuttles depart every thirty minutes or so and are free of charge.
As mentioned, if you arrive early enough, you can ignore all the signs along the road telling you about the mandatory shuttle. As you’ll observe upon your arrival, the shuttle system is in place to avoid parking limitations outside the Frijoles Canyon Visitor Center.
Unfortunately, there are no public transport options to Bandelier National Monument, as you’ll still have to drive quite a distance to reach the shuttle departure point.
Before visiting any site run by the National Park Service, it’s always a good idea to check the official website for the most recent updates. You can find Bandelier National Monument’s page here.