Taking the bike on the bus or train is generally permitted in Bremen – provided you have a valid ticket. For more information on travelling by train with a bike, visit the website of the local public transport provider VBN. You'll find ticket information and terms and conditions for Bremen's public transport network on the BSAG (Bremer Straßenbahn AG) website.
There's also useful information for cyclists on the Deutsche Bahn website.
You can even take your bike on many of the Weser river tours.
Quelle: WFB Wirtschaftsförderung Bremen GmbH/T. Vankann