We present muon spin rotation and relaxation (µSR) measurements on the noncentrosymmetric superconductor PbTaSe2. From measurements in an applied transverse field between Hc1 and Hc2, we extract the superfluid density as a function of temperature in the vortex state. This data can be fit with a fully gapped two-band model, consistent with previous evidence from ARPES, thermal conductivity, and resistivity. Furthermore, zero field measurements show no evidence for a time reversal symmetry breaking field greater than 0.05 G in the superconducting state. This makes exotic fully gapped spin-triplet states unlikely, and hence we contend that PbTaSe2 is characterized by conventional BCS s-wave superconductivity in multiple bands.