>What is a dollar "based on"?
It's a coupon tradable against a portion of the future production of the entire US economy. As long as the country makes anything, and as long as the government is around, a dollar one owns is tradable for items produced there. For it to fail would take tremendous failure of likely the entire world economy, at which point all promises of future trade will be suspect. As such, it's quite stable for the foreseeable future.
What is a bitcoin based on? It's currently also tradable for goods to those offering to take BTC for goods directly (a tiny and shaky market), or more tradable to those willing to give dollars for BTC, which is bigger, but still tiny and shaky compared to a dollar itself.
BTC marketcap $62B USD, ~$5B daily trading volume. USD trades ~5T a dat, and likey does a few T more in business transactions/day.