Bush also took on his rivals for the nomination for not directly attacking Trump in previous debates.
In an interview with CNN's Chief Political Analyst Gloria Borger, Bush deemed Trump's boycott "kind of weird" and claimed that "it'll hurt him that he's not showing up in the Iowa debate, four days before the Iowa caucuses."
The former Florida governor also called out his fellow Republican presidential candidates for being "very afraid of dealing with" Trump in other debates, but predicted Trump's absence could change the dynamic on stage in Des Moines come Thursday.
"They've been in the witness protection program, and now they may come out," Bush said, referring to his opponents' decisions to not directly take on Trump in past debates, which have shattered ratings records for cable news networks.
Bush claimed that Trump's decision calls into question the Republican front-runner's ability to serve as commander in chief.
As president, Bush said, "You got to make tough decisions, you have to challenge things, you have to deal with foreign leaders that don't all agree with you. You can't take your toys and go home."
Bush, despite lingering in the single digits in Iowa and battling for second place in New Hampshire, insisted that he did not have to win the Granite State and that he was in the nomination fight for the long haul.
"We have a national campaign, we're on every ballot," Bush said, making clear that he does not view the coming contests in Iowa and New Hampshire as crucial to victory. "It's a long process. It isn't all concentrated in two or three states."
Bush also downplayed how the campaign has impacted his relationship with his Republican rival, Florida Sen. Marco Rubio.
"Marco can handle it, I can handle it" Bush said. "We're going to be friends at the end of this, and we'll see how it all plays out."