On your right is the Green Dragon pub, not one I frequent, but another King and Barnes house. The site of the old King and Barnes brewery is further away, also to your right. Regrettably, K & B were taken over by Hall and Woodhouse and the brewery closed.
To the left is the Merrythought Restaurant, a great little restaurant, open during the day, but not the evening, serving mainly English food. Just the place for a late breakfast.
Walking a little further west along the Bishopric is the Kings Arms, another King and Barnes pub. I've always liked this one for a quiet drink, although there is a danger of being nailed to the dart board on the way to the toilets.
Finally, although not in the Bishopric itself, but a little to the North of the Shelley monument, is the Malt Shovel public house - a good spot for to sample an ever changing range of guest beers with landlord Steve and his staff. Click on the picture to go to the pub website which describes the pub far more effectively than I can