Bunsen was  born in Göttingen, Germany in 1811, in what is now the state of Lower Saxony in Germany. Bunsen was the youngest of four sons of the University of Göttingen's chief librarian and professor of modern philology, Christian Bunsen (1770–1837).
After attending school in Holzminden, Bunsen matriculated at Göttingen in 1828 and studied chemistry with Friedrich Stromeyer, mineralogy with Johann Friedrich Ludwig Hausmann, and mathematics with Carl Friedrich Gauss. After obtaining a PhD in 1831, Bunsen spent 1832 and 1833 traveling in France, Germany, and Austria. During his journeys, Bunsen met the scientists Friedlieb Runge (who discovered aniline and in 1819 isolated caffeine), Justus von Liebig in Giessen, and Eilhard Mitscherlich in Bonn.