Hi Intaglio,
Bridging between two objects makes the new polygon part of the object where you start from. In that way you need to start from your character model and not from the “external” object. You should see the problem instantly when you check your new polygon with the weight manager.
I haven’t worked with “bridging” and character tools, but there is a feeling that tells me to not add polygons while the object is bind to joints. All weighting needs to be checked at least. See image. I used the —-> and <—- to indicate from which object I took the initial edge to “bridge”.
To answer the question from a pure modeling point, I was able to use bridge on a “skinned” object without switching it this option (skin) off. If that is a clean workflow, I’m not certain, as the variety of options might be endless.
(I checked as well to use an initial edge on the skinned object and bridged it to another edge on the same object. It worked and the weighting was nicely included. If that is for all situations (weighting) possible, needs to be checked carefully, as weighting is the “life” of the character. I use normally other tools than bridging for work on the same object, it is too easy to miss a point or points)
Good luck with the project
Sassi