At the University of Bath, there are lots of student societies, clubs, and events that you can get involved in. All student societies affiliated with the SU are required to adhere to an Equal Opportunities Policy, which you can read here if you’re interested. This policy ensures that students are protected from discrimination based on (among other things) their sex, gender identity and trans status.
You may sometimes see events advertised as being gender-specific. (For instance, in 2013 the SU advertised a self-defence class “for women.”) Nonetheless, because of the Equal Opportunities policy, all students are free to participate in any of these events regardless of their gender identity, gender presentation, medical, legal, or trans status. If you have questions about this, or if any issues arise which cannot be resolved by speaking to the person/society that organized the event, you can speak to the LGBT+ Trans Rep or any SU Officer.
However, note that not all Student Societies are officially affiliated with the SU, including several of the religious societies. This means that they are not required to adhere to the Equal Opportunities Policy, and so may have different attitudes towards trans inclusion. Students need to discuss this with unaffiliated societies on an individual basis. If you would like support in doing so, the LGBT+ Trans Rep will be happy to help.