Might be a better way, but if it was me…
From temple meads head along clarence road (keep the river on your left), onto commerical road, follow that along till you pick up the cycle patch by the river off cumberland road (is obvious), follow that all the way along to the bridge over the river that’s half blocked off (dunno it’s name, again it’s obvious, by the warehouses etc). then follow “festival way” cycle path signs that take you past the alotments and into the bottom of ashton court. Climb up the hill to the trails.
That make sense?
EDIT: this http://goo.gl/maps/KgWjv
but i’d cross the two roundabouts like a pedestrian to cut them out.