The University Bristol Union (UBU) has 53 sports clubs of which 20 are recognised as Focus Sports Clubs (docx, 17KB). A Focus Sports Club is eligible for additional support in order to compete at the highest level of student sport. One of the benefits of this is that you'll be covered by UBU's Personal Accident Insurance.
UBU also has a number of sportier societies including martial arts clubs, outdoor activity groups and wellbeing activities - check out the society pages for more information.
If you're not a student at the University of Bristol you'll need to take out Associate Membership of UBU (£25 per year). This will automatically happen when you join the clubs (and societies) you have chosen.