The source appears to be mostly St. Athanasius, who was a deacon in Alexandria at the time the Arian controversy broke out (and later the bishop of the same see). He writes in his Discourses Against the Arians (Discourse 1, Chapter 1, 4)
For of the one [i.e., a certain Sotades, who apparently wrote songs] has Arius imitated the dissolute and effeminate tone, in writing Thaliae [The Banquets, songs that Arius wrote so as to be sung at banquets]; on his model; and the other [i.e. the daughter of Herodias] he has rivalled in her dance.
Who, after abandoning the oracles of divine Scripture, call Arius's Thaliae; a new wisdom? And with reason too, for they are announcing a new heresy. And hence a man may marvel, that, whereas many have written many treatises and abundant homilies upon the Old Testament and the New, yet in none of them is a Thalia found; nay nor among the more respectable of the Gentiles, but among those only who sing such strains over their cups, amid cheers and jokes, when men are merry, that the rest may laugh; till this marvellous Arius, taking no grave pattern, and ignorant even of what is respectable, while he stole largely from other heresies, would be original in the ludicrous, with none but Sotades for his rival. For what beseemed him more, when he would dance forth against the Saviour, than to throw his wretched words of irreligion into dissolute and loose metres?
So, it seems that Arius composed songs that sailors could easily remember. (It is to be recalled that Alexandria was a major port city.) This seems to be the reason that Arianism spread so quickly, whereas previous heresies had remained largely contained in local areas.