Are there discount tickets in Bremen for PhD student in Germany?

There are typically no discount tickets for students in Germany.

As student, you get a 'Semsterticket' together with your matriculation documents after payment of your semester fee. This ticket allows you to use public buses and trains for free within the state, except long range trains like IC/EC/ICE.

Since Bremen is a small state on its own, the range of its Semsterticket ticket is extended to about half the area of the state Niedersachsen, and also includes some IC trains between Bremen and Emden / Norddeich.

For more details about where the ticket is valid, see this link (scroll down for english version)

https://www.asta.uni-bremen.de/service/semesterticket/

Of course, you do pay for the semester ticket with the semester fees.
At my university, PhD students are not required to be matriculated. For many PhD students, the benefits like free public transport and other student discounts did not make up the fee, so they do not matriculate. So, if you decided against it, you have no ticket.

If you have a Semsterticket, you need to put your photo in it, and in addition, need to have your ID card with you.

German public transport typically only offers single tickets in standard fare or child fare with a child being under the age of 15. Since a university student is most likely port than that and doesn’t look young enough, they won’t be able to chat their way into a child fare.

Long-term passes often come in additional flavours such as senior citizens or students. Whether you qualify for a student discount depends on the local terms and conditions. When I studied in Munich, the confirmation of matriculation of the local university essentially sufficed to buy weekly and monthly passes. For school students, a confirmation of the school of typically needed.

Many university cities (and even Munich now, having been one of the last) now also have a semester ticket for their students which is essentially a flat rate you pay on matriculation to use public transport for the entire semester. Often this semester ticket is valid in a much larger area than just the city; e.g. a semester ticket of the University of Hannover is valid in all of Lower Saxony, Bremen, and trains into/out of Hamburg and Kassel (but only local transport, not long-distance trains).

However, both the options above require you to be a student of a local university. There are no provisions for students from elsewhere (not even other places in Germany) to pay lower fares when showing an ISIC or equivalent. So essentially the answer is: if you aren’t studying there, there is no student discount.