I have read that the Due and Bridge will work with the (now obsolete) Yun Shield or Dragino, et al. I have numerous versions of the YUN, Rev0, the .org board and Rev2. However the DUE has many features I desire to use for more complex sketches in the same eco-system as the YUN where I have many already on my local network. It seems that if one ties the 32u4 reset to ground on the YUN, which apparently tri-states all data pins on the 32u4 I should be able to use the LINUX part of the card connected just like the shield to the DUE. Has anyone got a clue if this is practical? I don't think I would mesh all of the pins on the cards together, but rather just use ground and the UART pins, D0 & D1. I do understand that the DUE USB port must be used for programming. Comments and/or experience much appreciated.
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.