The "cliched" image of a bomb is based on explosive devices that were basically pots made of clay or metal filled with gunpowder and a wick jutting out. They're the precursors to modern day grenades and have been used in battle frequently since the 17th century. While a modern bomb doesn't correlate with the stereotypical image, grenades from previous centuries do.

The grenade has been around a lot longer than dynamite. Due to the longevity of the grenade it is the image that is most prevalent in popular media. Also grenades have been used by various extreme groups as a shock tactic. The anarchists of the late 19th century and early 20th used grenades on a number of occasions (especially in France) which stirred up a moral panic regarding anarchism and the bomb. Additionally Tsar Alexander II of Russia was assassinated by a left wing terrorist organisation using a bomb device. Events such as these have engrained the stereotypical image of the bomb in our culture.

http://www.telegraph.co.uk/news/uknews/1455110/Battlefield-gives-up-1689-hand-grenade.html - Description of a grenade from 1689

Edit: Extra information