Rope bridges see a lot of repetitive action over a small span. I would not put a biner on a bridge unless it was fairly necessary. Most of them have rough edges that will repeatedly abraid and pick the short section of rope. Additionally, it increases the capacity to load the gate, and/or rotate the locking mechanism - one more piece of complexity. Rings are standard and very simple. So is the abr radius, which is compact and has a big bend radius. The rook gets mixed reviews - usually due to their long length (bad), bulky volume and weight (bad), big bend radius (good), swivel action (good), multiple attachment points to simultaneously use multiple climbing systems (good), and smooth pulley action (good). Girth hitching a sling to the bridge is likewise better as a temporary measure due to repetitive friction on the same small length of rope, plus the loss of the intended functionality of the bridge as a work positioning assist. The petzl ring is attachable, but you'll need to inspect the screws regularly. Good luck, be safe, replace your bridge as appropriate and replace it correctly.
