I’m going to have to agree with what some others have said here. The problem is highly unlikely to be with the bridge if a replacement doesn’t solve the issue (although there is the small possibility that you got two faulty bridges).
That suggests that there is something wrong with the DAC itself - just because it functions fine on other inputs doesn’t mean anything, it could be a problem with the Bridge interface part.
Send both back and ask for a new DAC with a new bridge that have both been tested and confirmed by PSA not to have any clicks or pops when they use them.
I think it is worth trying if you really like the DAC. - This is purely anecdotal since it is a sample size of one, but I have never had any such problems with my DS/Bridge2 combo at all despite having a highly resolving system. So it is possible to have both in your system without these issues.