Bombs have been around for centuries. The military units called "Grenadiers" in European armies used throwable black powder bombs, early versions of what today are called grenades. They were heavy, so Grenadiers were tall, strong soldiers able to throw grenades for a distance. Terrorism has been around for many centuries, most infamously the period called The Terror (1793-94) in the French Revolution. However, the combination of bombs and terrorism is considerably more recent, dating to the 1870s and 1880s.
Black powder had been used occasionally for terrorism before the 1800s, with the most famous incident being the Guy Fawkes gunpowder plot to blow up the English Parliament in 1605. Fawkes used barrels of gunpowder rather than a bomb in the modern sense. Terrorism was nothing new in the United States, where, for example, tarring and feathering of Loyalists during the American Revolution was a terror technique designed to quell Tory sentiments. However, terrorists using bombs to accomplish political ends in the United States goes back only about 150 years. That's partly a result of the rise of political movements seeing violence as legitimate, and partly the result of the development of dynamite.
Alfred Nobel invented dynamite in 1867, making usable a substance that had been invented years before, called nitroglycerine. The substance was known to be a powerful explosive, but it was too unstable and too dangerous to be of much use, until Nobel devised a way to make it stable and usable. Nobel also invented the blasting cap, which would ignite the dynamite, using a fuse that could be lit, and later, allow it to be ignited by an electric charge provided by a battery. Nobel would late in his life feel remorse for the harm his invention had caused, and established the Nobel Prizes as a kind of atonement.
