Was John Bardeen the only person to win two Nobel Prizes in his or her field?

Yes. John Bardeen (b. 1908) won two Nobel Prizes in physics.

In 1956, he and W.B.S. Shockley and W. H. Brattain were awarded the prize for the invention of the transistor.

In 1972, he and L. N. Cooper and J. R. Schrieffer were awarded the prize for developing the BCS theory, which uses physics to explain superconductivity.