Your visa, which was issued by the German diplomatic representation in your home country, is usually valid for three months, and has the status of a temporary residence permit. Before these three months have elapsed you will have to extend the visa for 12 or 24 months. If your initial visa is valid for the whole time of your studies in Bremen, you will simply have to report to the authorities ("Ausländerbehörde" - public authorities responsible for aliens) at the beginning of your stay.
This authority is responsible for renewing visas, and may amend your visa if you are accepted to switch to a different study programme. If you move to another town you will have to cancel your registration with the public authority responsible for aliens in the town you are leaving, and re-register with the office in your new place of residence. If you move within the same city, simply update your resident's registration within a week.