alt Hacker NewsCopenhagen has fairly decent public transportation and biking is quite common.
Bikes are allowed basicly everywhere: https://dinoffentligetransport.dk/en/how-to-travel/bicycles-...
Caveat: Bikes are not allowed in the Metro during rush hours 07:00-09:00 and 15:30-17:30. But it is allowed the rest of the time and has 24H service.
You should also know that the greater Copenhagen area is covered by "S-Trains" which are running on dedicated (not mainline) tracks. So metro-ish.
The S-Trains have dedicated space for bikes: https://youtu.be/hgfOxNRAktI
So even bumblebees can fly if you let them.
Actually taking a bike on the Copenhagen metro is rare, in my experience, except very late at night when it's empty anyway.
It is almost as annoying to others as taking a bike on a bus.