I think Bitcoin might start appreciating more once it can no longer be mined, or the buyers per mined coins increases..so as more and more people invest in bitcoin and less and less coins are being mined then we may see another big trending upwards. I don't know but that's how my little logical brain would put it. Just my 2 bits.. 
I think your thinking in wrong direction, if more and more businesses accept bitcoins and create a natural demand for coins then we may need to mine more to meet the demand right? Also as of now lot of coins are with traders hand hence they will trade every day to make some profit with those coins, it makes it more unstable. When more businesses and normal people holds these coins then it will appreciate and it will more more stable price.