Bush spent a few minutes in their locker room before practice. He said he was able to talk to his favourite team, calling them "the mighty Mustangs."
Moody Coliseum is across the street from the former president's library and Bush lives in Dallas, not far from the SMU campus. He and wife Laura, whom he described as a "big SMU fan", have attended some games.
"They're exciting, they play hard, and they made the big time," Bush said. "Hopefully they can go a long way."
When asked how far he thought SMU could go in the tournament, Bush said he's no pro at prognosticating basketball. He also has no plans to fill out a tournament bracket.
"On the other hand, I do know a good team. They've got a good team, care for each other, they play hard," he said. "I told them it's the hottest ticket in Dallas it seems like right now, and it's fun to watch them. I really do wish them all the best."
Coach Larry Brown said Bush congratulated the team and told them how proud he was of them for playing together.
"Every time Laura and President Bush show up to our arena, the whole environment changes in such a positive way," Brown said. "He's a positive person and we all look up to him, and to know he would take the time out and support us, that was pretty special for all of us."
SMU plays UCLA, one of Brown's former teams, in the South Region on Thursday in Louisville, Kentucky.
"We'll be watching," Bush said. "Since I'm retired, I'll have a little time in the afternoon on Thursday."