{We report time-resolved terahertz spectroscopy measurements of the electronic transport properties of dilute GaAs bismide and nitride alloys. The electron mobility for GaAs1-yBiy (y=0.84%) extracted from Drude fits to the transient complex conductivity was similar to 2800 cm(2)/V s at a carrier density of 2.7x10(18) cm(-3), close to the mobility of 3300 cm(2)/V s measured for GaAs at a similar carrier density. The electron mobility did not decrease significantly for Bi concentrations up to 1.4%. In contrast, the GaNxAs1-x (x=0.84%) and GaNxAs1-x-yBiy (x=0.85%