He stopped Aaron while he was leaving the field after a pregame ceremony honoring former owner Bill Bartholomay, who moved the Braves to Atlanta. As Aaron was leaving the field, Bourn ran over and introduced himself before the legend was able to get away.
"I just wanted to shake his hand," Bourn said. "I didn't want an autograph, none of that. Just, 'Nice to meet you, you did a lot for the game, home run king.' He told me, 'Keep going hard, keep working hard.'"
Bourn said he was happy he got a chance to play in the Civil Rights Game for the first time. Before the game this year's Beacon Award recipients -- Hall of Famer Don Newcombe, Earth, Wind & Fire and Congressman John Lewis -- were honored and Bourn said it was important to recognize their accomplishments.
"A lot of those players did a lot for the game," Bourn said. "They paved the way for us, people like me, [Jason] Heyward, [Matt] Kemp, everybody that's an African-American that's been able to play the game of baseball."
Heyward agreed with his teammate's sentiments. He played in last year's Civil Rights Game, which was also held in Atlanta, and said he was glad to have had the opportunity.
"It was really fortunate to be a part of a situation where we're recognizing civil rights and what baseball's done for that," Heyward said.
The Civil Rights Game festivities also included a luncheon honoring the Beacon Award winners. Dodgers first baseman James Loney, who homered in the Dodgers 6-2 victory Saturday night, was in the audience when Newcombe, a former Dodgers pitcher, received the award.
He said he enjoyed the whole day.
"I went to the luncheon, saw Newk get his award," Loney said. "It was great seeing Hank Aaron, guys like that. It's real special what they did for the game."
Bourn said he wanted to pay respect to what players such as Newcombe and Aaron did for today's generation. His father taught him the importance of recognizing those that came before you, and Saturday was Bourn's chance to honor the civil rights trailblazers that made it possible for him to play in the Major Leagues.
The pregame moment Bourn shared with Aaron is one he will cherish for the rest of his life. He said he looks forward to telling his two-year old son, Bryson, about the moment one day in the future.
"That's something you know you won't forget," Bourn said. "As you get older, you can tell your kids. They won't know who he is because unless he pulls off a miracle and God wants him here, he'll be gone to another place.
"It was a pleasure to meet him."
Teddy Cahill is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.