Tidal streams of disrupted clusters are routinely detected in the halo of the Milky Way. It was recently shown that tidal streams of open clusters can now also be detected within the disc. In this work, we highlight the fact that tidal streams provide a powerful new diagnostic of the non-axisymmetric disc potential and may provide a new constraint on the pattern speed of the Galactic bar. In particular, we show how the stream-orbit misalignment for an open cluster on a quasi-circular orbit in the solar vicinity varies as a function of the position w.r.t the bar resonances. The angular shift rises beyond corotation, reaching values as high as \(30^\circ\) close to the outer Lindblad resonance (OLR), then dropping again and reversing its sign beyond the OLR. We applied this mechanism to the recently detected the Hyades stream. We note that the stream would be very similar when taking a potential with no bar or with a fast pattern speed of 55 km.s\(^{-1}\) kpc\(^{-1}\). However, we find that the stream is different than previously detected when adopting a potential with a bar pattern speed of \(39\) km.s\(^{-1}\) kpc\(^{-1}\). Previously detected Hyades candidate members would, on the other hand, favour a barless or a fast bar galaxy. Interestingly, the previously reported asymmetry in star counts within the leading and trailing tails of the Hyades tidal stream persists in all cases. Our study conclusively demonstrates that the effect of disc non-axisymmetries cannot be neglected when searching for tidal streams of open clusters and that current candidate members of the Hyades stream should not be trusted beyond a distance of 200 pc from the cluster. Moreover, our study allows for ideal targets to be provided for high-resolution spectroscopy follow-ups, which will enable conclusive identifications of the Hyades stream track and provide novel independent constraints on the bar pattern speed in the MW.