There are a number of colleges with the name Trinity College. In order to acquire accurate information, the particular college in question needs to a identified in detail. That being said, whether the degree is approved or recognized is up to the receiving institution, in this case Bristol University. You can contact Bristol University by going to the below listed link.
http://www.bris.ac.uk
Trinity University of Asia was created in 1963.
Trinity Western University was created in 1962.
Holy Trinity University was created in 1940.
Trinity Southwest University was created in 1990.
Trinity International University was created in 1897.
Trinity University College was created in 1848.
Trinity Washington University was created in 1897.
Trinity Washington University is located in the state of District of Columbia.
Leeds Trinity University College was created in 1966.
Nancy Pelosi went to Trinity Washington University (BA)
It is a University.
That would be Trinity College - The University of Dublin