Don't know the underpass you mention, so not commenting on that.
I guess my point was cycling in Bristol is pretty good, in spite of lack of infrastructure - maybe even because of lack of infrastructure, with what little I've seen making things worse as a rule; Bristol Bath path / Strawberry line excepted- those are rather good. Even the A38 towards Aztec is fine to cycle along with the daily pelaton to work managing just fine on a dual carriageway with very few "out of my way" beeps for those of us sticking to the road / flyover etc.
There is a comically stupid bit of cycle lane on said A38 towards town where you are expected to go from a speedy (40mph limit, presumably 20+ cycling) through a 1m wide chicane, stop dead, then cross the slip road. I'd be astonished if a single cyclist has ever done this. Might take a photo for the Warrrington lot at some point.