On Know Your Place you can check out old maps of Bristol. Sadly there doesn't seem to be an easy way of linking to a particular map/location. Still, here's a little screenshot of the 1898-1939 layer. These tracks are still there on the later 1949 map, so at least this section survived the war, I think.
Having checked Wikipedia I think this section, which ran from Canons Marsh to Ashton Avenue Bridge and then on to the south was created in 1906, and closed in 1965.
This map fragment will be © Ordnance Survey.