Use the alternate route!
Rode to Monte Cristo on a sunny Saturday. Arrived to a packed TH at Barlow Pass at 8:30am. Parked about 1/4 mile from the parking lot along the road. We chose to ride in on the main trail, but if I were to do it again, I would ride the alternate route both ways. More about that below. The log crossing is currently superfluous as the river it crosses is dry and can be easily walked across without getting shoes wet. The log looks sketchy for schlepping a bike and we heard someone fell off it with a bike later that day. Passed dozens of groups along the way, but we were one of the fist groups to arrive at the ghost town and had the place largely to ourselves for over an hour. Hikers were beginning to arrive as we wrapped up our visit. Rode back on the alternate route.
Notes:
1. Bring a lock if you want to explore! We didn't realize that bikes aren't allowed past the first meadow and ended up pushing ours since I wasn't going to leave them unsecured. Exploring would have been much more fun without them, but this area is super crowded, and I wouldn't leave them unlocked. There is a bike rack in the meadow.
2. Take the alternate route both ways. The main route is crowded, and the short section of single track is understandably designed for hikers and not a ton of fun to ride. The log crossing is sketchy, and the whole trail is crowded with hikers. We took the alternate route on the way back and we only saw 1 other rider. There are a couple of punchy climbs on the way in, but otherwise it's a nice road.
3. Park at the alternate TH, 3/4 mile past Barlow Pass. There were hundreds of cars on our return to Barlow Pass, and only 2 at the alternate TH with room for dozens of cars.