Q is actually M.Bison on life support. What I mean by that is, in SFA3 his Psycho Power strength was insane, however things like changing his body ended up weakening his power, and he ruthlessly wants to be more powerful until he's unstoppable. At some point in his life though after SF4, he struggled so much to become so powerful that he just couldn't keep control of the Psycho Power anymore, and that would cause his ultimate death if he couldn't find a solution to that (and by that, I mean no resurrection or stuff like that).
Without his powerful abilities the Shadaloo organization is coming to an end, but also his own life is coming to an end, so he had to come up with a way of surviving while still keeping the essence of the Psycho Power. This is where the iron mask comes in, this makes Psycho Power to be only used in a low, stable level, but in exchange this keeps him alive well (and I use the word "well" very loosely).
Shadaloo has been destroyed, and now Bison is all alone, on the run to find a way to become powerful again while keeping his appearance as low-profile as possible (until he finds a way to become the all mighty Bison again). This could explain why Shadaloo just doesn't seem to exist anymore and Bison's absence during the events of SF3.
Also, his rival is Akuma... now I'm not sure if it's canon that he killed Bison in SF2, but it's kinda eerily with this theory in mind.