The former Florida governor will visit Germany and also tour Estonia and Poland -- two former Soviet-bloc states that offer an easy platform for criticism of the Obama administration's policy towards Russian President Vladimir Putin.
It should be an easy mission for an accomplished politician -- a quick flit across the pond to bolster foreign policy credentials ahead of a likely presidential campaign.
But Bush should choose his words with care if he is to avoid extending a dubious streak that has seen Republican candidates tumble into controversy overseas.
Mitt Romney, the 2012 presidential nominee, endured a disastrous trip to Europe three years ago and committed a huge gaffe by questioning Britain's readiness to host the London Olympic Games on the eve of their taking place.
Romney tried to roll back his criticism but was openly mocked in front of a huge crowd by London Mayor Boris Johnson in unflattering video footage that was beamed back to the United States.
Romney also went to Poland and suffered the indignity of reporters yelling at him to answer for his missteps -- before a top campaign aide was caught on camera telling the press pack to "kiss my a**."
Romney's disastrous sojourn earned him the unwelcome headline "Mitt the Twit" in the merciless British tabloid press.
This election cycle has not been kind to potential presidential candidates who venture across the Atlantic either.
Louisiana Gov. Bobby Jindal also managed to irk Johnson when he claimed in January that some areas of Europe, including parts of Britain, had become Muslim "no-go zones."
New Jersey Gov. Chris Christie, meanwhile, found out earlier this year that answering questions abroad about boiling political issues back home can also get you into trouble.
Christie said that parents should have a "measure of choice" about whether to vaccinate their kids, drawing charges that he was equivocating to appease evangelical conservatives.
Wisconsin Gov. Scott Walker made his own trip to London this year and dodged a question on whether he believed in evolution -- and managed to steer clear of deeper distractions by avoiding questions on pretty much everything else.
Perhaps wisely, Bush is avoiding London, where journalists like nothing more than tripping up visiting American presidential candidates.
Had he braved the wrath of the British media, Bush would likely have faced unwelcome questions about his brother, former president George W. Bush, and the Iraq war, both of which remain deeply unpopular in the U.K.
His visit to Germany will recall then-Sen. Barack Obama's trip to Europe during the 2008 presidential campaign, which saw him deliver a soaring speech before a crowd of hundreds of thousands euphoric Germans in downtown Berlin.
But even Obama, who was wildly popular in Europe, didn't escape controversy. German Chancellor Angela Merkel was apparently annoyed at his campaign's request for him to speak before the iconic Brandenburg Gate, where President Ronald Reagan once cried, "Mr Gorbachev, tear down this wall!"
Obama did not get that privilege until his second term, in 2013, by which time he was much less popular in Europe and, as a consequence, drew a much smaller crowd.