We present C and X-band radio observations of the famous utraluminous X-ray source (ULX) Holmberg IX X-1, previously discovered to be associated with an optical emission line nebula several hundred pc in extent. Our recent infrared study of the ULX suggested that a jet could be responsible for the infrared excess detected at the ULX position. The new radio observations, performed using the Karl G. Jansky Very Large Array (VLA) in B-configuration, reveal the presence of a radio counterpart to the nebula with a spectral slope of -0.56 similar to other ULXs. Importantly, we find no evidence for an unresolved radio source associated with the ULX itself, and we set an upper limit on any 5 GHz radio core emission of 6.6 $mu$Jy ($4.1times10^{32}$ erg s$^{-1}$). This is 20 times fainter than what we expect if the bubble is energized by a jet. If a jet exists its core component is unlikely to be responsible for the infrared excess unless it is variable. Strong winds which are expected in super-Eddington sources could also play an important role in inflating the radio bubble. We discuss possible interpretations of the radio/optical bubble and we prefer the jet+winds-blown bubble scenario similar to the microquasar SS 433.