Yes, Bitcoin's price may increase further. We have seen that the price of Bitcoin was in good condition for the last few months and we can expect more from Bitcoin. Many believe that the price of Bitcoin will grow again at the end of June so we can expect a bit more from Bitcoin.
Most investors are expecting only one thing from Bitcoin - its growth. Very few people really need it for anonymity and safe transactions, however, the latter characteristics can be really improved in the future.