The samples showed levels of radioactive caesium-137 that are 14 times higher than samples of honey from elsewhere in the UK, prompting scientists to call for an investigation into wider contamination at the site.
The plant, which closed in 1994, no longer produces nuclear energy. It is still in the process of being decommissioned, however.
Independent nuclear energy consultant John Large said bees are an important barometer of environmental health.
"Bees are key indicators of what is happening in the environment."
Trident trap: Replacement of nuclear subs 'to cost ยฃ167bn, exceeding all expectations' https://t.co/eWKlzVvWjx pic.twitter.com/SwE51uBCjwโ RT UK (@RTUKnews) October 25, 2015
They forage in a three-mile radius around the hive and anything in the soil is drawn up into plants and into the nectar they collect.
"This reading is within the limit for human consumption, but caesium-137 should not be turning up in honey at all," he added.
The results are included in the government's Radioactivity In Food and the Environment report, published last week.
A spokesman for the Scottish Environment Protection Agency said the radiation level poses little danger.
"The concentration identified is low and is not a cause of concern for the public or the environment," they said.
However the contamination will cast a shadow over the government's renewed emphasis on nuclear power.
It was announced in October the UK had signed a deal worth ยฃ2 billion which will see the Chinese government invest in the Hinkley Point nuclear power station. The deal has been heralded as the beginning of a new collaboration between Britain and China on the construction of more nuclear power plants.
Speaking in Beijing at a joint news conference with China's Vice-Premier Ma Kai, Chancellor George Osborne expressed his delight at the new
UK/Chinese deal.
"We want the UK to be China's best partner in the West. [This guarantee] paves the way for Chinese investment in UK nuclear [to help provide] secure, reliable, low carbon electricity for decades to come."
Energy Secretary Amber Rudd also told the BBC nuclear power is paramount for Britain's energy security.
"We want low-carbon electricity and if we're going to hit our ambitious [emissions reduction] targets then we have to have nuclear," she said.
One anonymous security official told the Times in October the Chinese deal poses a threat to national security.
"There is a big division between the money men and the security side," the security source said. "The Treasury is in the lead and it isn't listening to anyone โ they see China as an opportunity, but we see the threat."
#2 : Even under normal operational conditions there are leaks in most nuclear facilities. Unfortunately as the demand for more and more electricity continues more nuclear power plants are being built, the reasoning being that even in a major accident we have the technology to neutralize "escaped" radiation.
#3 : The pioneers in nuclear energy production are the French. They practically produce enough energy from their nuclear power plants to cover the needs of most European Nations. They also and here's the important part are currently constructing the first in the world nuclear power plant using water.
Why is it so important ? Simple. I'll give you an example : A glass of water is enough fuel for the lights of Paris for 1 year. It's a super efficient way of producing electricity. We are talking about 10 to 20 of them would be enough for powering the entire Eurasian continent for decades with just a few gallons of water/year. The rest of the continents on the planet of course will follow.
#4 : Suddenly , the other day NASA officially declared that they discovered a water glacier on Mars.
Needless to say that since the first manned mission for Mars is scheduled to depart in about a decade from today, they knew about the glacier at least 20-30 years ago, they simply figured it would be better to keep it classified. Most likely they are going to use it to produce electricity and drinkable water. The alternative would be to produce electricity from Mars' soil but that is not a desirable option as it's close to producing electricity from fossil fuel. It's outdated.
That's about it, I got a bit carried away as usual, but I think that was important info.