Here, in templemeads, is a bus to relish. Yes its small, no, it doesnt run weekends, but its free. It can take you from the station to the BRI, the highbury vaults pub at the top of Saint Michael's Hill, and the General Hospital by the harbour and the Ostrich Pub. Which means you could use it during a weekday pub crawl, perhaps.
The bus can be used to get between Temple Meads and Cotham. We've no data on whether it is faster or more reliable than the #8 bus for this, but it does have a cost advantage. Students and patients only though. There are no obvious checks, but a family with holiday luggage may have to do some explaining.
The University has a map and timetable.