In reply to Natasha_thePanda:
Avon Mountaineering Club are one of the most active climbing clubs in the country, with trips most weekends, plus the membership fee gets you BMC insurance, which on its own is pretty much the same price. I imagine a great place to meet a good mixture of people; both sport and trad climbers, those of differing ages, abilities and experience. https://www.avon-mc.org.uk/calendar/
The above facebook group is the biggest for finding climbing partners in Bristol, however you'll no doubt receive an usually large number of replies from overly keen males!
You could also message my friend Robyn (username 'crowter'), as she networks with a lot of female climbers in Bristol.