The real reason for my trip to Beijing was not to bicycle around the city - that was an artifact of scheduling constraints for what I really wanted to do: hike a remote section of the Great Wall of China.
Note that I said "a remote section"; what I wanted to avoid was the Badaling section of the Great Wall that most tourists to Beijing visit. That can look like this:
Instead, I found Great Wall Hiking (https://www.greatwallhiking.com), run by travel entrepreneur, Gary Lee, which offers a number of group and custom hiking experiences on a sections of the Great Wall about 85 miles north of Beijing. Some of these experiences include camping overnight on one of the ancient watchtowers!
Many of the group hikes require a minimum number of hikers to sign up, or the hike won't happen. Since my trip was a one-shot deal, I couldn't risk a cancellation, so I opted for one of the custom hikes that are guaranteed to happen. In my case, I chose the "Small Group Iconic Great Wall Hiking" trip which includes 2 days of hiking on remote sections of the Great Wall and an overnight (with meals!) in a small hotel next to the Great Wall.
I was picked up at my hotel by Great Wall Hiking's friendly and professional driver, Jason (Liang):