Banning rifle and pistol ammunition would be clearly un-constitutional. If you read the militia laws in effect in the 1700s they specify that all men beteen the ages of 16 to 65 (or 16 to 60 in some cases) MUST posses a military shoulder weapon AND a specified amount of ammunition.
Curiously enough, it might be legal to ban shotgun ammunition because most of the milita lows prohibited anyone from passing inspection with a "fowling Piece"(eg A shotgun.)