The planes had been stationed at RAF Fairford, the preferred European base for US bombers, and had recently been used in US strikes on Iran.
Last week, five UK men were arrested near the base - which Iran's Revolutionary Guards previously said was a legitimate target - on suspicion of preparing terrorist acts.
"So, what you saw there is the Secretary of War, out of an abundance of caution, trying to protect our guys," Vance said as he left Washington DC for a trip to Alaska.
"We do feel with some confidence that the Iranians are, you know, they're trying to do what the Iranian state has done for 49 years, which is engaged in acts of terrorism against the United States - and others - so we are being extremely cautious, and that's all I'd say about that."
Earlier, US Secretary of State Marco Rubio said there was no direct link between the sudden removal of the bombers and the suspected Iranian plot.
He said the Pentagon is "constantly reallocating resources where they need to be".
A NATO military source had said on Monday: "It is still believed that Iran poses an acute threat to US assets in the UK".
While much about the incident remains unexplained, UK Prime Minister Andy Burnham said any plot was likely backed by Iran.
Iran has said accusations that it was involved in any plot are baseless, and Foreign Minister Abbas Araqchi wrote on X: "I can confirm Iran's belief that releasing supposed terrorists working for foreign states really says it all. You're barking up the wrong tree."
Rubio said on Monday the United States had confidence in the security of all its bases.
Fairford, located 145km west of London, is one of the most important in Europe for the US, being one of only a few suitable for heavy bombers such as the B-1 aircraft.
It has played a key role in previous US campaigns in the Middle East, although its bombers are not stationed there permanently.
During the current conflict, the US had permission to use Fairford only to strike Iranian missile sites that were attacking ships in the Strait of Hormuz, or so-called defensive strikes.
The United Kingdom had refused permission for the US to use its bases for offensive strikes on Iran.
A Pentagon official confirmed on Sunday that all US bombers which had been deployed to Fairford had headed to their home stations in the US.
The Pentagon said the US bomber force remained ready to deliver precision global strike capabilities "anywhere, anytime".
The New York Times, citing two US officials, said the US had rushed over the weekend to move the bombers after commanders received new threats about an Iran-backed plot.
It said some of the planes had left while aerial refuelling aircraft were still being scrambled.
Christoph Bergs, research analyst at defence think tank the Royal United Services Institute, said the redeployment would in the short term reduce US capacity "to quickly surge sorties against Iran, reducing the threat level somewhat".
But he noted that use of Fairford was already limited given the UK's stipulation on defensive strikes.
The aircraft could now potentially be sent to either Diego Garcia or bases in the Gulf, to reduce the need for more air-to-air refuelling to cover the additional distance, but that would depend on capacity availability, negotiations with allies and security, he added.
In the early hours of September 27, five London men in their 20s were arrested after being seen running into fields from three white vans parked near the base.
Police said no explosive devices were found but a quantity of petrol was present.
The men have since been released on bail.
A sixth man, a dual UK-Iranian citizen arrested on suspicion of preparing terrorist acts four days later, has also been released on bail.
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