You are right that the Bible doesn't say there were three magi, and also right that it doesn't say they were kings.
The folkloric idea that they were kings is odd. The text says what they were. They were...magi.
(As you probably know, the word "magi" has the same root as the word "magic". Magi are magicians, not in the "I can pull a rabbit out of a hat" sense, but in the sense of being sorcerers, wizards, or astrologers, those who claim special knowledge or special powers.)
A related odd idea, common in folklore but not supported by the Bible, is the notion that the star they followed was exceptionally bright. It's brightness is never mentioned in the text http://www.biblegateway.com/passage/?search=%20matthew%202:1-11&version=ESV