For me it is too early for Bitcoin to stabilize at this point. its volatility is still causing the roller coaster rise and fall of the price in the market. I don't think it will stabilize anytime soon but if you think about it it is what makes Bitcoin stronger as well. In time I know Bitcoin price will stabilize but not anytime soon.
The market of cryptocurrencies especially the market of bitcoin needs more years in order to mature and to lessen the volatility because from the start until now, most of the time the only thing that makes the price of bitcoin more fluctuates is the news which is a very huge reason why the price of any cryptocurrency can move up or down but i think after a few years, this type of market will not be like that and it will be more stabilize and more on technical analysis rather than fundamental.