The number that matters, and where to find it
The figure to look for is the indoor unit's sound-pressure level in dB(A) at the lowest fan speed, measured at 1 metre. Manufacturers report several noise figures on the spec sheet; the one that governs a bedroom install is that lowest-speed figure, not the nominal or maximum. A top-tier Japanese wall-mounted split will report 19 to 22 dB(A) at low fan; a budget European unit typically reports 26 to 32 dB(A). That gap is the difference between a unit you forget is on and one you notice every time the room settles into quiet.
This is one small piece of the bedroom AC decision, which also depends on sizing, install position and orientation.