I live in a small city in Sweden, about 30,000 people, having just moved here from a larger city of about 100,000 nearby. Many, many people here do everyday stuff by bicycle, very similar to nearby Copenhagen in that respect.

None of the very-well-used and very-well-planned buses have racks on them. A bike tends to be the speedy alternative to the bus, so it makes sense in some ways. Most of the trains can accommodate some bikes if they're not too overcrowded, like they were for most of the summer. Starting this week, the number of trains has nearly doubled, so it's much easier to do this. You do have to buy a child's ticket for it, though...