That's nothing. Apparently there are some out there who still do things like ride horses, make their own bread, sing songs, and drink alcoholic beverages. Join the 21st century already, people!
You wouldn't have the hydrostatic shock that a bullet provides, but if the grey matter disruption of a small-calibre round to the head is sufficient to drop a zombie, a heavy draw bow and a broadhead oughta work, too--and the arrow might be more re-usable than a bullet.