Even with a stable price Bitcoin won't ever be able to hurt the us dollar. We must accept that Bitcoin is only here to function as an alternative, where we benefit from features as storing our wealth outside the banking and governmental system. You can send money to any part in the world instantly without the need of a third party service. Not so much an interesting option anymore due to the higher fees, but Bitcoin lends itself also nicely to be used as a currency tool as in buying stuff. Governments are the only entity to force through a change in their fiat system. Bitcoin can't even make a dent in this case
I tend to disagree with that point
If Bitcoin starts being used as a means of payment, it will necessarily compete with, say, dollars. Some goods and services that were formerly exchanged for dollars now will be exchanged for bitcoins. That means that these dollars will be used as payment for other goods, and overall more dollars will be chasing less goods (since some goods will be exchanged for bitcoins). If Bitcoin use as a means of payment remains tiny, it wouldn't be a big deal, but if things get serious, that will lead to inflation in dollar prices of goods and depreciation of the dollar itself