If you are willing to pay an agency your housing search time will be reduced. Usually agencies have the most attractive offers. You won't have anything to do with the landlord since the agents take care of all the administrative tasks. When agents help you find a flat they will charge a fee (Courtage). This usually goes up to 2 month rent (Kaltmiete) plus additional charges and taxes. An estate agent may not ask you for any payment until you legally sign a contract. Never pay a fee, not even a handling fee before a lease is signed. Also, never sign a contract until you fully understand it and everything has been properly negotiated.
Here are some links to agencies in Bremen area:
And for the Vegesack area (close to campus):