I can't speak about the compatibility of the Bridge library with the Due's SAM processor. But that doesn't seem to be your question.
You want to disable the '32U4 so that you can connect D0 and D1 from the Yun to the Due using some jumper wires, so that the Due can talk to the Linux processor. While I haven't tried it, I can't think of any reason why this shouldn't work (assuming that the Bridge library works on the Due, which doesn't seem to be a concern of yours.)
I don't think it's necessary to hold the '32U4 in reset. I think it would be easier to load a sketch into the '32U4 that sets D0 and D1 as inputs, and does NOT call Serial1.begin() or Bridge.begin(). That should accomplish the same thing as holding the '32U4 in reset, and still allow using it for other things, if desired. It won't be able to use D0, D1, Serial1, or the Bridge library, but all of the other pins should be fair game.