You asked me earlier if I used a Network Bridge with my Vivaldi.
I think what you are really asking without saying it is; Would I get a benefit by using a Bartok plus a Network Bridge?
The answer is that whatever benefits that using a separate Bridge may bring you also have to consider that the Bartok is dCS’ entry level DAC.
There is no point in improving the network board if the following DAC cannot take full advantage of it.
My own view is that the appropriate upgrade is not to add a Bridge to the Bartok but to upgrade to a Rossini.