Thanks for your message John. I've come across the following directory entries for the 'other Ostrich'
1879. Charles Triggle, Lower Guinea Street
1883. William Windows, Lower Guinea Street
The address of the Ostrich at the time was 28 Guinea Street, everything to the left of the pub had a lower Guinea Street address. I wonder if the other Ostrich was part of the Ostrich but with a separate licence, perhaps in the small building to the left. It might be worth looking at the magistrates Court quarter session records for licence applications, at the Bristol records office.
Incidentally, Charles Triggle and William Windows can also be found in the list of licencees for the 'Velindra' just around the corner.