The "GSM noise" (intertoob search hint) or its more recent variation has made a come back. For the first few years of G2 service hearing the "dut, dut, duuuuuutttttt" was common as presenters put their phones in their coat pockets, right next to the lavaliere mic wire. Some phones had enough RF output to cause the same noise in lectern mics as well. What does the noise sound like, can you capture a recording?
I do not think this is AC power related (sorry, Rob P). A UPS, while useful for mixers and such, only benefit products that would experience a reboot time if power were lost and restored quickly. If you have a genuine AC mains power quality issue, and it happens everywhere you use your system (like, more than just in your shop or garage) you have a device or cable problem as Rob suggests but it is not caused by the power company's service.
Did you purchase the Bose new or used? If used, perhaps there is an internal issue (not familiar with it at all) and that's why it was for sale.
Depending on your answers to Rob and I, I'll probably have some other questions later.
Edit ps: Welcome to Soundforums, just noticed this was your first post!