When did Barnabas go looking for Saul?

Barnabas went looking for Saul at the right time, when he saw that God was beginning to deal with Gentiles. It was not accidental; he intentionally sought him out, found him, and brought him back to Antioch, where they ministered to the Gentile congregation for eighteen months.

Les explains that Barnabas was God's man at the right time. When he saw that God was beginning to deal with Gentiles, Barnabas went looking for Saul. It was not an accidental meeting; he intentionally sought him. After finding him, Barnabas brought Saul back to Antioch, and the two ministered there to the Gentile congregation for eighteen months. This period preceded the transition into chapter 12, where the narrative shifts back to Jerusalem and Peter.

Did Barnabas go looking for Saul or did he just accidentally run into him?

Barnabas deliberately went looking for Saul; it was not an accidental meeting. He sought Saul out, found him, and brought him back to Antioch, where Paul and Barnabas then ministered to that Gentile congregation for 18 months. The context shows an intentional search, not a chance encounter.