Try this.. Bubble Qyzen, turn off all his attacks but 1, send him to engage a ranged fighter. When he does damage, send him to fight something else.
As soon as the threat level Qyzen generated on the initial DPS dissipates, it will switch agro to you, even if you do nothing.. It's easy to test on mobs several levels below you, and Qyzen will take a good chunk of health from them.
Also, in PVP matches, if your bubble "absorbs" a 2.5k hit, you will get the 2.5k heal medal even if you haven't casted a single heal spell. Pretty much a free medal at the start of each pvp match (and especially in huttball when they get pulled into the fire, the ticks are >2.5k)
And what you said makes sense (about bubbling people while running by). I've done this too, and what I've noticed is that if they are engaged (i.e. the targets are grey to you), they will not attack you unless your threat goes above the other person. And even when the person dies, they still remain in an engaged state for awhile and wont attack you. But I think that's more of a glitch, or by design.