<p>We study the dynamics of a massive scalar field in the background of the Hayward black hole, which can be interpreted both as a regular spacetime and as an effective geometry arising from Asymptotically Safe gravity. The quasinormal spectrum and grey-body factors are computed using the WKB method with Padé improvements and confirmed through time-domain integration followed by Prony analysis. We find that the mass of the field significantly suppresses the damping rate of quasinormal oscillations, giving rise to long-lived modes that continuously approach arbitrarily long-lived states (quasi-resonances) at certain critical field masses. In the time domain, the standard exponentially decaying ringdown is replaced by oscillatory tails with a power-law envelope. The corresponding grey-body factors reveal a pronounced shift of the transmission peak toward higher frequencies and a suppression of the low-frequency part of the spectrum. Finally, we show that the correspondence between quasinormal modes and grey-body factors remains valid for massive fields, being highly accurate for large multipole numbers and gradually losing precision as either the field mass increases or the multipole number decreases.</p>