Regardless, the former Vol is enjoying his rampant popularity, even if he thinks "The Mayor" nickname is a bit much.
"That didn't come from me, and I don't deserve it," Bradshaw said, smiling sheepishly. "We've got too good of a mayor in town as it is."
Although he may not relish the nickname, the former Vol certainly understands it.
"I'm always selling something, signing something or kissing babies, so the public address announcer (Brian Tate) started calling me The Mayor," he said. "I guess I look like a politician sometimes but that's not for me."
Even with a limited interest in politics, Bradshaw is adept at getting votes. He was among 20 players selected for Tennessee's All-Century Team in 2008 balloting by fans and a university-appointed selection committee. He averaged just 4.8 points and 3.5 rebounds per game for his career, so the recognition was a testament to his team spirit, hustle and dedication.
Although he always kept the game in perspective, Bradshaw admits that the end of his college career was a strange experience.
"It felt weird because I woke up on a Saturday morning and, for the first time since I could remember, I didn't have to go lift weights or shoot or run," he recalled. "It was kind of different. You move on, work hard at other things and try to still stay involved in basketball. I get to do that through basketball camps and some media things that I do. It's a lot of fun still giving back to the game."
This summer he's "giving back to the game" twice a week in the Rocky Top League, being one of the key players for the Knoxville News-Sentinel entry. Incredibly, he plays with the same level of enthusiasm he exhibited as a collegian.
"It's a blast for me - somebody who doesn't get to play full-court basketball anymore," he said. "I know it's not the most important thing in the world but, for me, it's a blast to try and stay in shape so I can get out here and play with these guys again.
"You don't take the game for granted while you're playing but you certainly miss it when you're done, so it's fun for me to get back out here."
Because he still follows Tennessee hoops closely, Bradshaw was eager to see Vol signees Jordan McRae and Trae Golden in Rocky Top action. After facing both, he believes they're going to help the Big Orange.
"They both really impress me," Bradshaw said. "I haven't seen Trae as much but Jordan really has a mature demeanor about himself on the court and a high basketball IQ."
Originally from Memphis, Bradshaw has settled in Knoxville to begin his business career.
"I'm in pre-paid sales of gift cards," he said. "We started our own company, and I'm trying to get that off the ground."
Basketball remains a big part of his life, though.
"I'm doing basketball camps during the summer and a little bit of commentating (for Knoxville radio station WNML) during the season," he said. "I'm hoping to get my foot in the door and do some more things."
You should be able to do just about anything you want when you're The Mayor.