I am visiting Copenhagen for the first time and would primarily like to use a bike to get around since, as I understand, that's what you do. I found Bycyklen, which seems good because I won't need to worry about theft, and bike rental places can be kind of scummy in my experience. I have a Citi Bike membership and use it frequently in addition to my "real" bike so I'm familiar with bike share.
Is this a good way of getting around for a tourist? (for example, Citi Bike is a pretty big ripoff for non-annual members) Are there any caveats I should know about? (I once had a bad time getting an American credit card to work correctly with Velib)