Actually, that's not the original meaning of the word.

Most of the dictionaries give it as deriving variously from the Spanish or Italian buscar/buscare/boscar ... ultimately to seek ... in the 19th century.

There was, however, already an English verb to busk (it appears in the 1828 Websters Dictionary, for example) meaning to be busy or to go around busily. It is still (rarely) used ... as in "He busked about".

:-)