"Look, the future president of Argentina (Cristina Fernandez de Kirchner) would be good for one beer; yours (would be good) for four," Copeland reportedly told the magazine.
"I was mortified to learn this remark reached you and you were asked to comment on such a trivial matter," the musician wrote to Bachelet.
"If by chance you are able, Sting, Andy (Summers) and I would welcome the opportunity to personally express our admiration for you and your wonderful country by extending an invitation to you and your guests to attend our performance," Copeland wrote.
Bachelet has yet to respond to the apology or the invitation.
2014: The Year in Music [PHOTOS]