By bus
Busses are widely available. The company for the busses is called delbus (http://www.delbus.de, german). The central bus station ZOB - Zentraler Omnibusbahnhof is located next to the central train station. Normally every bus stop has it's own map of the bus system. There is one schedule for the weekday "Tag", every 15 min. and another one for evenings and weekends "Freizeit", every 30 min.
The pricing system is connected to the over-regional VBN Verkehrsverbund Bremen-Niedersachsen, Travel Association Bremen-Lower Saxony. Prices may have changed, look here for more information (http://www.vbn.de/en/tickets/01-vbntarif.shtml, english). Adult starts at â¬1.60, depending on the zones you travel through. Don't mind to ask, but don't expect everyone to speak English.