I think it's also the removal of the constant stimuli competing for your attention with other forms of transportation. If you take a train, you're probably looking at your phone, or trying to catch up on something on your laptop en route. If you drive, you're likely listening to music, ads on the radio, an npr piece talking about something you like, etc.

Being on a bike, your priorities shift to keeping yourself alive occasionally, but mostly just thinking while moving forward. It's generally a good place to solve problems for me too.