Adam Clarke on Acts 19:8

Spake boldly - three months - We have often remarked that St. Paul, in every place, made his first offers of salvation to the Jews; and it was only when they rejected it, that he turned to the Gentiles; see Act 18:6. And the same line of conduct he pursues here: he goes to the school of Tyrannus, at least a public place, to which all might resort, when they obstinately rejected the Gospel in the synagogue.

Disputing and persuading - Διαλεγομενος, και πειθων, Holding conversations with them, in order to persuade them of the truth of the doctrine of Christ.