This is a bullion coin sold for its metal content; the $1 denomination is artificial. Silver is currently selling for about $16/oz.
The Proof 2001 ASE has a current average retail value of $39.00.
Assuming you have a large coin with a picture of Miss Liberty walking and the sun in the background, you have a bullion coin sold for its silver content and not for spending. The dollar denomination is artificial. At the current price of silver it's worth about $17.
Gold plating a coin does not increase its numismatic value. It adds very,very little to the bullion value.
All US coins dated 2001 have the word Liberty on them, a denomination is needed.
If you mean a Proof 2001 American Buffalo dollar? Average value is $115.00.
It's still worth one dollar.
If you got it from a bank or as change it's just a dollar.
Believe it or not, it's worth exactly one US dollar.