Omnivorous writes:
I wish we knew how old they are.
Perhaps the smell is an indication?
But seriously, Dogmafood's suggestion seems unlikely to me, because that would mean that they would have popped up incredibly recently in comparison with the age of the Milky Way. We'd be very, very luck to be "around" when it happened.
I think the radiation itself doesn't emanate from the centre of the galaxy, but is the result of colliding gas clouds or some such thing. The extend of the bubbles would then not suggest an age of 24,000 years because the gas would probably be moving at much lower speeds than light speed (though still very fast, to account for the gamma radiation).
But I am no cosmologist, so don't take my suggestion too seriously.
"Ignorance more frequently begets confidence than does knowledge: it is those who know little, not those who know much, who so positively assert that this or that problem will never be solved by science." - Charles Darwin.