This is a chicken and egg situation. For bitcoin's price to stabilize, a large scale economy needs to develop with more businesses and users. For a large scale economy to develop, businesses and users will seek for price stability.
Fortunately, volatility does not affect the main benefits of Bitcoin as a payment system to transfer money from point A to point B. It is possible for businesses to convert bitcoin payments to their local currency instantly, allowing them to profit from the advantages of Bitcoin without being subjected to price fluctuations. Since Bitcoin offers many useful and unique features and properties, many users choose to use Bitcoin. With such solutions and incentives, it is possible that Bitcoin will mature and develop to a degree where price volatility will become limited.
In fact, in April 2016 Bitcoin's volatility reached record levels, close to that of gold, and other fiat pairs.