We present the results of bicoherence analysis on observations of GRS 1915+105 that exhibit quasi-periodic oscillations (QPOs). The bicoherence is a higher order statistic that can be used to probe the relation between the phases of a triplet of Fourier frequencies. Despite showing very similar power spectra, the observations exhibit different patterns in their bicoherence, indicating that the QPOs are phase coupled to the noise in different ways. We show that the bicoherence pattern exhibited correlates with the frequency of the QPO, the hardness ratio, as well as the radio properties of the source. In particular, we find that the nature of phase coupling between the QPO and the high and low frequency broad-band components is different between radio quiet, radio plateau, and radio steep conditions. We also investigate the phase lag behaviour of observations with QPO frequency above 2 Hz that show different bicoherence patterns and find statistically significant differences between them, indicating a change in the underlying physical mechanism. Finally, we present a scenario whereby the cooling of the jet electrons by soft photons from the accretion disc could explain the observed correlations between the bicoherence and radio properties.