We present an archival search for transient gravitational-wave bursts in coincidence with 27 single-pulse triggers from Green Bank Telescope pulsar surveys, using the LIGO, Virgo, and GEO interferometer network. We also discuss a check for gravitational-wave signals in coincidence with Parkes fast radio bursts using similar methods. Data analyzed in these searches were collected between 2007 and 2013. Possible sources of emission of both short-duration radio signals and transient gravitational-wave emission include starquakes on neutron stars, binary coalescence of neutron stars, and cosmic string cusps. While no evidence for gravitational-wave emission in coincidence with these radio transients was found, the current analysis serves as a prototype for similar future searches using more sensitive second-generation interferometers.