The only reason people traded their gold/silver for bills was because metals were hard to safeguard and inconvenient for trade. this is not true with bitcoin. Therefore no one would trade their bitcoins for "bitcoin bills" issued by the US government, except in very small amounts for convenience purposes (microtransactions, physical payments, etc)
Not "bitcoin bills." Rather, simply anyone could go to the bank and exchange their dollar or their bitcoin for, say, an ounce of silver. The point would be to place Bitcoin on an equal footing with the Dollar.
Of course, nobody would go to the bank and get an ounce of silver at today's bitcoin prices. But everyone would become a bit leery about obtaining more bitcoins for investment purposes when the bank was saying that they were willing to give them only the same amount of silver for a bitcoin as for a dollar. They wouldn't know for sure what other folks were doing. So, they would be a little slower to buy or trade for bitcoins.
Wouldn't this start to bring the dollar back up with relation to bitcoin?
No, only idiots would sell their coins for those reasons you mentioned. Also while some people might be that stupid in the US, the majority of volume is in Asia..
Also, it would make it too much of a hassle for helicopter Ben if the dollar was based on actual metals..