Speaking to reporters after holding a town hall here, Bush was asked whether he thinks Rubio, whose relationship with the former Florida governor goes back more than a decade, could beat Clinton next November.
"I'm a better bet," Bush said. "I got a proven record and I campaign in a way that's based on that record and based on ideas that I've had. I've been vetted. I've been tested. I'm an open book."
He argued Clinton wasn't as transparent and Republicans need to put up a nominee that can compete with her background. His comments echoed an internal memo from his campaign last month that labeled Rubio a "risky bet" because of his lack of experience and questions over his use of a state GOP credit card.
Earlier this week, The New York Times reported
that the pro-Bush group, Right to Rise, was considering a $20 million negative campaign against Rubio that included a strategy to paint him as too extreme on abortion. Rubio has stated that he's never advocated for allowing exceptions in abortion cases, like rape or incest.
Asked if he agreed with that strategy, Bush said, "I don't think anybody should attack someone who's pro-life."
Though Bush does favor allowing exceptions, he declared himself "the most pro-life candidate on that stage" and listed a number of steps that Florida took to try and limit abortions, like requiring parental notification and eliminating partial birth abortion.
Pressed further on whether he would disavow Right to Rise if the group ends up running ads against Rubio over his abortion stance, Bush repeated himself: "I don't think anybody should attack someone who's pro-life."
Although Bush didn't try to land any attack lines against Rubio in Tuesday night's debate over missing Senate votes -- as he attempted in the last event -- he resumed such criticism on Wednesday during the town hall.
"I think that people, when they show up, they ought to work. I just don't understand why that's such a complex thing," he said to applause at the event, which was held in a Coca-Cola bottling facility.
This time, however, he drew an analogy to a time when Bush could have possibly walked away from his job but didn't. In his final year as governor, he was being considered to be the next NFL commissioner.
"But I had nine more months to go (in his second term)," he said. "It didn't even cross my mind that I would leave early. I put my hand on the Bible that I was governor of the state of Florida to uphold the law, and that meant to me that it was from the beginning to the end. "
Bush was widely seen as delivering a stronger debate performance Tuesday night. With his drop in poll numbers, Bush had perhaps the most at stake and his campaign hired a media coach to help him have stronger command of the debate stage.
Last week, Bush told reporters that the coach was teaching him to not answer questions directly, but to use the time as a chance to get his own message out. Asked Wednesday if he felt that he should have adopted that advice earlier, given that it lead to a better debate performance, Bush grew candid and appeared to still be grappling with the new technique.
"I've had 62 years of life that's been jammed into my DNA that when someone asks you a question, you're supposed to answer it," he said. "In my time as governor, we had lively conversations with people in the press, and I didn't do a little you know kabuki dance around it, I took 'em on. Even our friends from the other teams, they come, I don't care, bring it on baby."
"That's the way I've been trained to do it, so now I'm learning the new art of acknowledging the question, being respectful of the questioner of course and then answering what's on my mind," he added.
Asked if that's a change from his gubernatorial runs in 1998 and 2002, Bush quipped, "That's a change from 1953 when I was a little baby."