Got carried away looking into other things in the area. https://www.openstreetmap.org/changeset/93312596

In the end I've just changed the access permissions on the bridge, since that should be sufficient to stop routers from using it, plus the bridge had incorrect access tags to begin with.

I'm not aware of any "closed public bridleway" (or other PRoW) tags.

I'd presume that the bridge should be fixed in not too long, due to lack of alternative PRoW routes (had to cycle along the A614) & that the bridleway to the north seemed to be well used. 