Hey Ukase,
Not a fool, there's a great deal of stuff to know about the game (I tend to forget most of it.. which isn't really useful, but how it works for me), so don't feel bad about not knowing about bruising, gauntlet usually gets talked about more.
As far as taking advantage of it, as discussed the other night on TankHQ, it is linked to your T1 attack, which as you stated is probably not the best for DPS. But, it should have the fastest recharge time (I think EM might be the exception to that), and the "debuff" lasts for 8 seconds. So, to take advantage of it, make sure you land a shot with your T1 every 8 seconds (or as close to it as you can) (save slots for other powers, or try adding procs (if you have slots available).
Other reading?
https://paragonwiki.com/wiki/Bruising