Yes, The Broadmead BID was established in 2005 and was one of the first in the country. Businesses have voted for a renewal of the Broadmead BID four times, receiving a stronger mandate each time. For more info see here.
The City Centre BID was established in 2017. Both of these BIDs are managed by Destination Bristol. There are also BIDs in Bedminster and Clifton Village. For more info see here.