The Cameroon international completed a move to the former La Liga champions on Monday to link up with his former Gunners teammate Cesc Fabregas, who switched to the Nou Camp last summer.
"It was not easy to bring Song to Barca," said Bartomeu. "As happened with Cesc [Fabregas], Arsenal did not want to sell him and were asking a high price, but we are happy with what we paid both for Cesc and Song.
"The negotiations weren't easy, but the player wanted to come, and that made things easier. It was tough, but it all went much faster than other negotiations have done."
The 24-year-old made the move to the Catalans three days after Robin van Persie abandoned the Emirates for Manchester United.