When you say he is using his music, you are referring to Fascinate, correct? That ability is listed as (Sp), which makes it a spell-like ability. Anti-Magic Field is the effect that the central eye duplicates, which blocks all spells, SLAs and supernatural abilities. Also as to your comment about not knowing where the effect originates, Fascinate requires targets to be able to see and hear the Bard.
For the sake of answering the question, no Beholders don't have ears. According the Lords of Madness, the book concerning aberrations, they state on pg 38 "Beholders typically have a dozen small tympanic membranes at almost random spots across their bodies; each is merely an inch in diameter and impossible to see except upon the closest examination." So no ears in the sense we picture them, but they can hear just fine.