In 1735, British poet Alexander Pope lamented, in rhyme, being besieged by "a parson much bemus'd in beer." The cleric in question was apparently one of a horde of would-be poets who plagued Pope with requests that he read their verses. Pope meant that the parson had found his muse—his inspiration—in beer. That use of bemused harks back to a 1705 letter in which Pope wrote of "Poets … irrecoverably Be-mus'd." In both letter and poem, Pope used bemused to allude to being inspired by or devoted to one of the Muses, the Greek sister goddesses of art, music, and literature. The lexicographers who followed him, however, interpreted "bemus'd in beer" as meaning "left confused by beer," and their confusion gave rise to the first modern sense of bemuse above. The newer (and common) use of bemuse to mean “to cause to have feelings of wry or tolerant amusement” is a topic of some dispute, as discussed here.

Are amused and bemused synonyms?

Many people link bemused with amused, believing that the former word carries the meaning “amused, with a touch of something else.” While this was not its original sense, bemused has been used in such a fashion for long enough, and by enough people, that the meaning “having feelings of wry amusement especially from something that is surprising or perplexing" has become established. You may use bemuse in this fashion if you wish, but bear in mind that some people find it objectionable, insisting that bemused and amused are entirely distinct and that bemused properly means “marked by confusion or bewilderment.” It is worth noting that before bemused indicated confusion it had the meaning (especially among poets) “devoted to the Muses.”