North Korea has conducted numerous missile and nuclear tests, including launching rockets over Japan.
The US bombers had taken off from the Andersen Air Force Base in Guam.
It was part of a "regular deployment training" aimed at enhancing the capability of implementing the "extended deterrence" against the North, the JCS said.
In an obvious show of force over the continued missile activities of North Korea, led by Kim Jong Un, the U.S. military has flown two strategic bombers over the Korean peninsula.
The US military statement said the exercise "demonstrates how USA military forces in the Indo-Asia-Pacific are always ready to defend the American homeland and how the USA stands resolutely with Japan and the ROK to honor their unshakeable alliance commitments".
Suspicions that Pyongyang may have stolen intel from South Korea will do nothing to de-escalate tensions with the United States, which are already at a 50-year high following the North's rocket tests.
Senior diplomats of South Korea and the United States will hold a vice-ministerial strategic dialogue next week in Seoul, South Korea's foreign ministry said Wednesday.
After entering South Korean airspace, the two bombers carried out air-to-ground missile drills in waters off the east coast of South Korea, then flew over the South to waters between it and China to repeat the drill, the release said.
But neither side is budging in the standoff.
A Pentagon spokesman, Colonel Robert Manning, said he was aware of the report, but declined to confirm or deny any aspect of it."I can assure you that we are confident in the security of our operations plans and our ability to deal with any threat from North Korea", Manning said."I am not going to address whether or not that [hack] has occurred".
While US Secretary of Defense James Mattis reiterated this week that diplomacy along with global economic sanctions would remain the leading element of US strategy towards blunting North Korea, military options were being prepared.
Reports of reconnaissance on USA utilities follow earlier reports alleging DPRK spies stole a large cache of military documents from South Korea, including a plan to assassinate North Korea's leader, Kim Jong-un.
Guam, from where the B-1 bombers in Tuesday drills departed, has been a particular target of North Korean threats.
Trump, on Monday, on Twitter said that a quarter century of US policy towards North Korea had been unsuccessful.
Separately, the Navy said a US submarine that is capable of firing Tomahawk cruise missiles and torpedoes made a port call Saturday at the USA base in the South Korean city of Chinhae. North Korea needs time and proof to believe that abandoning its nuclear programme will contribute to its own political and economic advantage.