The oldest records of bilingualism comes from the Old Babylonian period, in which we have both Sumerian and Akkadian versions of texts sitting side-by-side. See Hannes Galter's "Cuneiform Bilingual Royal Inscriptions"1 for more information there. During this period, too, we have letters written to kings in Akkadian where either a) the sender or b) the addressee did not speak the language of hand. This would require translators. Unfortunately, I am not aware of any specific translation notes around this time.
As far as a historical person who was bilingual or records of learning languages, the Greek Hecataeus of Miletus (6th/5th century BCE) claims to have spoken with Egyptian priests, which would require bilingual translators. Herodotus also implies that Scyles (less legendary than the also-mentioned Anacharsis) was bilingual. Ctesias appears to know Akkadian, as his history and the cuneiform records match.
Because bilingualism was such a common occurrence in the Ancient Near East and Mediterranean, most cases of bilingualism are implied, rather than directly stated.
Unfortunately, fi12 is wrong in his claims: Panini was neither the "father of modern linguistics" nor is he the earliest bilingual/multilingual historical persona. In fact, he might not even be older than Plato, who already had written on grammar, naming the sentence and distinguishing nouns from verbs, although it wasn't until Aristotle (still somewhat early in the fourth century, and probably a contemporary of Panini) who went into any scientific detail.
1From Izre'el & Drory edd. Language and Culture in the Near East, IOS XV. Brill, 1995.