Wikipedia opines that polyglot is in fact a valid word in these circumstances, and for a speaker of many languages there is the word hyperpolyglot. It also says that for two languages or three languages, bilingual and trilingual do “fit the bill”. Multilingual fits too, although I think I would prefer to reserve that for more than three languages since there is a word trilingual.
However, -lingual is an adjectival form and you would have to describe someone as being bilingual or a bilingual person. Bilinguist doesn’t really work, and nor does diglot (you would need the Greek di- prefix to use with -glot).
One might coin the words oligoglot or paucilinguist for someone who can speak a few languages, but I don’t think either will catch on.
So if you don't want to use bilingual then you are left with polyglot and multilingual.