If the US dollar crashes, bitcoin will most likely crash. This is because most of the bitcoin users are from the US, and with them gone, bitcoin will basically be much, much cheaper, as the americans try to sell their coins to get some sort of cash. Or maybe BTC will go up, they will try to convert their money into bitcoin, and cause a huge price spike.
It will have the opposite effect. People from around the world and in the US will see the inflation in the US and they will try to protect himself by buying gold, silver and of course bitcoin as well.
No one in their right mind will sell their bitcoins to buy a currency that is going through a hyperinflation. Keep in mind that people can shop with bitcoins and every business will start accepting bitcoins if their customers want to. So the entire dollar economy can shift pretty quickly to gold, silver and bitcoin.