Why won’t my Apple Watch record my stationary bike riding?

The first (and simplest) thing to try if something isn’t working right is to restart your Apple Watch and its paired iPhone. If necessary (device not responding), try a forced restart. Both methods can be found here:

How to restart your Apple Watch - Apple Support

Restart your iPhone - Apple Support

If that doesn't help, the next steps would be to unpair and pair your watch again and restore from the backup just created. This deletes all temp and corrupted files and re-indexes the file system.

Unpair and erase your Apple Watch - Apple Support

Set up your Apple Watch - Apple Support

I know this is probably obvious but just make sure you're selecting Indoor Cycling rather than Outdoor.