Fill the bill

I hear people say, "I'll foot the bill" as in "pay for it".

Today I heard someone say, "The Pres. Bush bobble head doll fits the bill".

Is "fits the bill" the correct phrase here?

As you say, to foot the bill is to meet the cost of something.
To fit the bill means to be be suitable. A bill would be a legal document rather than an invoice. An alternative is to fill the bill.
So the phrase seems to fill the bill here.