I have the BDAG Greek-English Lexicon in print, but do not own the electronic form. It's a little much to type out. So I'll just post a brief snippet and those who want to consult BDAG may do so at their convenience.
BDAG notes that BASILEUS denotes "one who rules as possessor of the highest office in a political realm, king, [generally] of a male ruler who has unquestioned authority (exceptions are client rulers who owe their power to the grace of Rome) in a specific area POIEIN TINA B. make someone king J[ohn] 6:15."
The word is applied to human kings, Christ, God and Abaddon (Rev 9:11).
I also found an interesting reference in LSJ where Aristotle calls the queen bee "BASILEUS." But there are good reasons why this fact does not necessarily prove that BASILEUS was used generically (of males and females) in ancient Greece or in Scripture.