The University has a transport plan on their website here - Precinct car parking | Transport Plan | University of Bristol. This includes links to parking information for University staff (including car-sharers), disabled staff and students, departments, contractors and visitors.
In addition, the following website is useful for information on public car parking: RingGo Cashless Parking Solution (myringgo.co.uk). For example, there is paid 4 hour parking on Tyndall Avenue near the Arts and Social Sciences Library, illustrated by this screenshot:
