I don't recall seeing a restroom with music in the background. Maybe in the airport restrooms!
But on the other hand, this feature is provided in many Japanese public women restrooms.
Many Japanese women are embarrassed at the thought of being heard by others during urination (see paruresis). To cover the sound of bodily functions, many women used to flush public toilets continuously while using them, wasting a large amount of water in the process. As education campaigns did not stop this practice, a device was introduced in the 1980s that, after activation, produces the sound of flushing water without the need for actual flushing. A Toto brand name commonly found is the Otohime (音姫, lit. "Sound Princess," also homophone with a legendary goddess Otohime). This device is now routinely placed in most new public women's rooms, and many older public women's rooms have been upgraded. The Otohime may be either a separate battery-operated device attached to the wall of the toilet, or included in an existing washlet. The device is activated by pressing a button, or by the wave of a hand in front of a motion sensor. When activated, the device creates a loud flushing sound similar to a toilet being flushed. This sound either stops after a preset time or can be halted through a second press on the button. It is estimated that this saves up to 20 litres (4.4 imp gal; 5.3 US gal) of water per use. However, some women believe that the Otohime sounds artificial and prefer to use a continuous flushing of the toilet instead of the recorded flush of the Otohime.
Source: Toilets in Japan