Is there an American bourbon that has no wheat?

The phrase "American Bourbon" is redundant; by law, bourbon must be made in the United States to be called bourbon. Most bourbon has no wheat. A typical bourbon MASH includes corn, rye, and malted barley. The legal requirement is a minimum 51% corn. Everything else is optional. Malted barley is used in small amounts (5%-15%) to aid in fermentation. Without it, enzymes need to be added to start fermentation. Rye is the more common flavoring grain. Wheat is more expensive (as a grain) but is used by a few bourbon brands, notably Maker's Mark, Weller, Fitzgerald, and the Van Winkle bourbons.