We present a new measurement of the bottom quark mass in the MS[over ¯] scheme at the renormalization scale of the Higgs boson mass from measurements of Higgs boson decay rates at the LHC: m_{b}(m_{H})=2.60_{-0.31}^{+0.36} GeV. The measurement has a negligible theory uncertainty and excellent prospects to improve at the HL-LHC and a future Higgs factory. Confronting this result and m_{b}(m_{b}) from low-energy measurements and m_{b}(m_{Z}) from Z-pole data, with the prediction of the scale evolution of the renormalization group equations, we find strong evidence for the "running" of the bottom quark mass.