First, you don’t appear to understand Gresham’s Law. For starters, it has nothing to do with the reason silver and gold are rarely used for transactions today (although it is the reason you won’t find a silver dime in your change anymore, and it will eventually lead to the demise of the penny.)
Second, wealth is rarely invested in currency. It is invested in assets. And while a dollar bill could be considered an asset, it is a poor investment because, like a bitcoin, it earns no interest. Unlike a bitcoin, it is relatively stable in value so it will continue to be favored by most businesses and individuals over bitcoins when used as a medium of exchange.
Third, compared to the bitcoin, the dollar is a paragon of stability. People have been disparaging the dollar for decades (with justification in the 1970’s), but it remains one of the world’s most popular currency for transactions.
Fourth, in my opinion, the bitcoin will fall into disfavor for any number of possible reasons long before the dollar does, unless Bernanke’s mismanagement of the Fed’s excess reserve position leads to a hyperinflation, as it could.
Obviously, or at least not at your level. ;)