There can be no talk about stabilization until the recent speculative bubble defuses. Stabilisation could happen in the less than 1$ range. A functional bitcoin ecosystem will bring about much higher velocity of money that, counterintuitively, will further depress prices. If 5 million bitcoins worth 1$ each change hands once every week, the annual GDP of the bitcoin economy will be 250 million $. We're far, far from that.
So when has the bubble begun in your opinion? February? Or at the first price spike to 50 cents?
Is it not possible that Bitcoin can simply evolve into a long term store of value, given its pre-defined, decreasing inflation rates?