But he tempered his comments by saying: "We should never do it in a way that pushes Russia away for a generation to come. Ultimately, Russia needs to be a European nation."
The Berlin speech kicked off Bush's five-day swing through Europe, which will also include stops in Poland and Estonia. It comes ahead of his planned Monday announcement in Miami of his bid for the 2016 GOP presidential nomination.
As he was en route to Europe, his campaign-in-waiting announced a shake-up, including the replacement of its expected campaign manager. The shuffle was seen as evidence that Bush's "exploratory phase" has not lived up to expectations that Bush would be in a commanding position over a large Republican field.
In his opening line in Berlin, Bush jokingly pleaded ignorance: "I don't know about the change in the campaign team. Guess I'll find out about that when I get home."
In choosing his itinerary, Bush focused "on allies who feel neglected by the Obama administration or who feel the administration hasn't done enough in response to Russian aggression," said Daniel Drezner, a professor of international politics at the Fletcher School of Law and Diplomacy at Tufts University.
Overseas visits have become part of the ritual for presidential contenders, especially those who have relatively little foreign policy experience, as they hope to reassure U.S. voters that they have the stature and fluency with international issues to hold their own on the world stage. Putin's aggression in Crimea, as well as the rise of the Islamic State, have once again put national security concerns near the top of the U.S. political agenda.
Bush is not the first in the increasingly crowded 2016 GOP field to visit Europe in the run-up to officially announcing. Their experiences have shown the potential pitfalls and the need to stay focused on a message.
New Jersey Gov. Chris Christie created controversy when he was drawn into a discussion in which he made ambiguous comments about vaccine safety. Louisiana Gov. Bobby Jindal gave credence to dubious claims that there are "no-go" zones in Europe where non-Muslims are not allowed. And Wisconsin Gov. Scott Walker spent a recent European visit deflecting questions about foreign policy - saying he believed it improper to comment on such matters while on foreign soil - even as he tweeted several remarks critical of President Barack Obama's approach to international affairs.
For Bush, there was one disjointed moment Tuesday. During his half-hour presentation, he brought up Iraq - a subject that has caused him trouble in recent weeks - during a stream-of-consciousness answer to a question about China's disputed claims in the South China Sea.
Bush compared the disagreement to the unrest in Iraq, calling it "an example of how voids are filled. As the United States has pulled back, for whatever reason, as we pulled back, the vacuum just doesn't stay. As we pulled back from Iraq, the vacuum still-."
He stopped himself, then backpedaled a bit.
"I don't think we pulled back significantly in Asia," he said. "But as we see in the sequester cuts, and the reduction in the naval forces that exist in the United States, and the tepid economic growth, it may be harder for our adversaries to imagine the United States to be in it for the long haul. As that climate exists, voids are filled."