He's fairly quiet. He doesn't waste words. He doesn't tell a lot of jokes. But it didn't take long for his fellow signal-caller to figure out that just because Bradford is quiet doesn't mean he doesn't have anything to say.
It's quite the opposite, in fact.
"When he does say something, it's worth hearing," Keenum said. "It's worth listening to and worth remembering. I do still remember quite a bit of what he shared."
Since signing with the Arizona Cardinals in March -- and especially since Arizona drafted Josh Rosen in the first round of April's NFL draft -- Bradford has been a mentor to the other quarterbacks on the roster.
When Rosen and Chad Kanoff, an undrafted free agent from Princeton, arrived in Arizona this May, Bradford, who is entering his ninth season on his fourth team, quickly told them to use him as a resource.
"I'm an open book, ask me anything, I'll give you everything that I've got," Bradford said he told them. "I've gone through quite a bit in my career, just as far as different offenses. I've seen a lot of different offenses, so I feel like I'm fairly knowledgeable in some of the schemes and some of the schemes that we're doing.
"I'm more than happy to help and just try to show them the way that I work, the way that I prepare, and hopefully they take something from that."
They already have.
Each of the three other quarterbacks, a group that includes Rosen, Kanoff and veteran Mike Glennon, are in various places in their careers as well as their development, so Bradford has been someone different to each of them.
Rosen has looked to Bradford for help on the nuances of football, Kanoff has leaned on him to learn about running an offense under center, while Glennon is getting help with unfamiliar concepts.
"He's super helpful in just about anything," Kanoff said.
Bradford has taken time out of practices and meetings to help the other quarterbacks -- especially the younger ones. He has quizzed Kanoff on the practice field, asking what he would do on certain plays with certain progressions against certain looks, both before and after a play. Kanoff, who ran a shotgun offense in college, said he has basically been following Bradford around trying to soak up everything he can. Sometimes Kanoff approaches Bradford with questions, asking how to hand off on a specific play, other times Bradford approaches Kanoff with a correction.
"It's like having another coach," Kanoff said.
Both Rosen and Kanoff have taken advantage of Bradford's knowledge and experience, Glennon said.
"They've been great so far as far as asking questions," he said. "And asking the right questions."
Keenum, the Denver Broncos' starting quarterback who was teammates with Bradford in Minnesota last season and in St. Louis in 2014, said Bradford has been good about talking through plays in the meeting room for as long as he has known him.
But that's where being on the quiet side helps Bradford.
He's not one of those guys who talks just to hear himself talk.
"He doesn't speak a ton, but when he does, you can tell he kind of has a plan and there's some logic behind it," Glennon said. "Some guys speak up about everything. Other guys only speak up when they feel it's necessary, and you could tell he does.
"And you can tell he's got a lot of knowledge about the game."
Keenum has always believed that when quiet people speak, it's usually to say something important. That's the case with Bradford, he said.
Cardinals tight end Jermaine Gresham, who has known Bradford since eighth grade, called Bradford the "cerebral assassin." Bradford is quiet, "but he has a killer mindset," Gresham added.
"I don't think he gets enough credit for it," Gresham said. "He just has that look like he's laid back, mellow but he has a side to him."
Keenum remembers Bradford being a resource on practically everything: protections, how to operate, where to go with the ball pre-snap and how to throw to certain positions, specifically tight ends.
"He's really smart," Keenum said.
Bradford shares that with his teammates, but Keenum said the best way to learn from Bradford is to watch him. Keenum said that's the best way for Rosen to learn from Bradford.
Rosen has been specifically working with Bradford on situational football, such as Arizona's red zone offense, how to call plays and handle tempo. Bradford said he's spent the most time with Rosen working on reading defenses and going through his progressions.
"He's helping me out a ton," Rosen said. "He's giving me a lot of pointers. I'm learning his play style, which is kind of unique. He gets the ball out of his hands really, really quickly. He is really thorough in everything he does pre-snap and he's definitely an awesome guy to look up to and learn from."
Bradford has already used some situations in practice as a teaching aid. There have been plays in which Bradford knew, from experience, that the first and second reads wouldn't be open, so he told Rosen to save time and skip to his third, he explained.
"There are a lot of nuances of the game some vets might know some tricks to," Rosen said. "I'm lucky enough to have them shared with me."
There's little doubt why Rosen was drafted: to eventually replace Bradford as the Cardinals' starting quarterback. But from what Glennon has seen so far, Bradford hasn't seemed reluctant to share his wealth of experience and knowledge with his successor.
"As far as I see, whenever Josh has something, he's willing to help," Glennon said. "That's the way I would be, too. Obviously, he's the starter and he's got to look out for himself first, but you would hope he would pass along the knowledge he has, and he does it."
Keenum believes Bradford will handle mentoring Rosen just like he handles, well, everything else.
Bradford's expression rarely changes, Keenum said, whether he nearly hits a hole-in-one or bogeys.
"He's the same guy all the time," Keenum said. "That's just how he's going to be. You have to understand that about him."
And even though Rosen will one day supplant him, Bradford appreciates the rookie's talent and ability.
"He's done a great job," Bradford said. "I think I've been impressed just with his ability to grasp things mentally. Coach has thrown a lot at all of us in trying to learn this system. It's tough for a rookie to be able to come in and understand everything that's being asked of him. I think he's done a tremendous job of that, and then physically, he's just really gifted. You can see he can make all the throws. He's got plenty of arm strength to push the ball outside the numbers, to push it downfield."