We have examined fine-structure mixing between the rubidium 5 2 P 3/2 and 5 2 P 1/2 states along with quenching of these states due to collisions with methane gas. Measurements are carried out using ultrafast laser pulse excitation to populate one of the Rb 5 2 P states, with the fluorescence produced through collisional excitation transfer observed using time-correlated single-photon counting. Fine-structure mixing rates and quenching rates are determined by the time dependence of this fluorescence. As Rb(5 2 P ) collisional excitation transfer is relatively fast in methane gas, measurements were performed at methane pressures of 2.5 − 25 Torr, resulting in a collisional transfer cross section (5 2 P 3/2 → 5 2 P 1/2 ) of (4.23 ± 0.13) × 10 −15 cm 2 . Quenching rates were found to be much slower and were performed over methane pressures of 50 − 4000 Torr, resulting in a quenching cross section of (7.52 ± 0.10) × 10 −19 cm 2 . These results represent a significant increase in precision compared to previous work, and also resolve a discrepancy in previous quenching measurements. arXiv:1812.09466v1 [physics.atom-ph]