The two dollar bill is available from banks, like the $1 gold-colored coins. You find $2 bills at racetracks, mostly. People tend to avoid them, because they're so easy to mistake for $1 bills.

Since the original problem omitted $2 bills, there doesn't seem any compelling reason to include them. But I submit that it's no less reasonable to make change with 50 $2 bills, as it is to do it with 100 $1 bills.