Thomas Bayes was born in 1701. Richard Price was born 22 years later, in 1723.
Price presented Bayes' Essay on Chances to the Royal Society in 1763, two years after Bayes' death. He wrote half the paper, and was the first to publicly apply the theory.
---
Stephen Fienberg traces the first use of the term "Bayesian" to R.A. Fisher in 1950.