Adequate health insurance is compulsory. Under German law every student is required to be adequately health insured. This holds also for visiting students spending just one or two semesters in Bremen.
If you are from an EU member state your home insurance usually will be effectual. If you come from outside the EU or are going to study permanently in Germany we strongly recommend to take out a public German health insurance, for instance at hkk, Barmer GEK, Techniker Krankenkasse (TKK), AOK etc. Please note that the contribution for students is fixed, no matter where you take out your public German health insurance.