BTC will surely continue growing and a time will come when all the people who want to control their money will shift to BTC and only leave a small portion of their funds in fiat. Right now you can already spend BTC on a lot of things, both physically and online and in the future it will increase.
However, i don't think there will be a time when people would not want to accept the u.s. dollar, it is such a strong currency and the u.s. economy is so stable, so i think both BTC and the u.s. dollar will be used together, but BTC will be used a lot less than it.