Tidal streams of disrupted clusters are powerful probes of the gravitational potential of the Galaxy, and are routinely detected in the stellar halo of the Milky Way. Recently, it has been shown that tidal streams of open clusters can now also be detected within the Milky Way disc, such as the Hyades stream. During this talk, I will present the recent results we obtain by exploring the impact that has the Galactic bar on the morphology and on the kinematics of the Hyades stream. Our results show that disc tidal streams such as Hyades provide a powerful diagnostic of the non-axisymmetric disc potential, and can in principle 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 varies as a function of the position with respect to the bar resonances. I will also present the impact that the potential fluctuations of the Galactic bar pattern speed can have on disc tidal streams, and how they can be used to measure the periodicity of these fluctuations, should they exist.