They do in Middle-Earth, though I think it is rare. But, if I remember correctly, in The Hobbit, Thorin Oakenshield shot arrows from the gates of Erebor at the messangers of the armies of Thranduil and the Lake-Men. So if the rightful king of the Dwarves of Durin used a bow, I think its safe to say that other dwarves did on occasion aswell.
But in Warhammer the dwarves don't use anything so low-tech as a bow.