While Bauer was being interviewed early Sunday morning over FaceTime, his number was visible on the top of the screen for a few seconds during a KBO game being shown by the network.
"It was an unfortunate mistake and we sincerely apologize to Trevor," ESPN said in a statement.
Bauer, an All-Star selection in 2018, decided to have fun with what he called a "massive screw up" by ESPN. He shared a screenshot with his number on the screen and said that rules for the giveaway can be found on his voicemail.
A few hours later, Bauer posted an update on social media, saying that his voicemail was full from fans reaching out to him. He later answered additional FaceTime calls from people and allowed them to ask one question.
The giveaway includes a pair of signed cleats and an autographed baseball, which Bauer said will be awarded over the next 48 hours.