One more note. When I disconnect the Rotel amp and use headphones through the BHP Pre jack I hear nothing. When I connect the Rotel I hear the hum through the headphones. I guess this reinforces the conclusion that the humm is caused by the BHK and Rotel not getting along.
I use Signal Cable interconnects. I can hear the hum from one foot away, farther if its really quiet in the room.
I had a similar issue. I went with trying -10db attenuators (fairly cheap) for each channel between the BHK-pre and my amp. I have fairly efficient speakers (93db), so that may have been part of the issue, but the attenuators almost completely got rid of the issue for me. Of course, I heard many say attenuators may degrade the SQ, but that was not my experience - at least that I can tell. Don’t know how I’d blind test it. Just something else you may want to try!
Have you got another pair of any kind, even the freebie patch cables that you can try and eliminate the cables as the source of the buzz.
Hey Guys, I tried unplugging and reseating the tubes in the BHK Pre and the hum went away. 
Not sure what to think about that. Hope it stays fixed. The gear is sounding great again. Thanks to all who offered advice. M
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Hi, I am new on this board and do not have pm privilege yet. I am having the same issue that you described, but only on the headphone site. Have you found a solution to this? I get a buzz when the volume display is on, but it gets much quieter when I turn off the display. My best guess is the issue with the headphone preamp. Let m know if you got this resolved.
I swapped the BHK with the preamp in my other system in another room, thereby enjoying new power connections, interconnects and loads. The problem totally vanished with speakers and was 95% cured on headphones. But because everything changed I can’t say which change cured the problem. HOWEVER, eighteen months after the swap, just two weeks ago, a similar problem recurred - a somewhat different noise (more hiss than buzz), also one channel only, but still independent of volume setting or source selection, and appearing worse with headphones. Changing the tubes and power connections did not help. This time swapping the BHK to a different system also did not help. My BHK is back in Boulder for repair.