The AA route finder gives the distance as 12.4 miles.
Bristol's metered cabs charge £2.60 for the first 218 yards, and 20p for each 218 yards thereafter. My calculator makes that come to £22.60.
Of course taxi drivers don't have to stick to the metered fares if they're travelling beyond the city boundary, so you should ask for a quote first.
Private hire firms are often cheaper. V Cars has a good reputation in the area. Call 01179 25 26 26 for a quote.
Chris