We present the first spectroscopic study of the host environments of Type Ibc supernovae (SNe Ibc) discovered exclusively by untargeted SN searches. Past studies of SN Ibc host environments have been biased toward high-mass, high-metallicity galaxies by focusing on SNe discovered in galaxy-targeted SN searches. Our new observations more than double the total number of spectroscopic stellar population age and metallicity measurements published for untargeted SN Ibc host environments. We discuss the path forward for making progress on SN Ibc progenitor studies in the Large Synoptic Survey Telescope era. This paper includes data gathered with the 6.5 m Magellan Telescopes located at Las Campanas Observatory, Chile.