Prince William fired an arrow during an archery session that went wayward, prompting him to say: "I hope I haven't killed the driver or that man on the bridge."
Kate, meanwhile, was forced to shout "so sorry" when a dart she threw during a practice session of the sport of khuru, or dart throwing, narrowly missed a group of women.
The small Himalayan nation's second-most popular sport was developed by cow herders, who would fashion large darts out of tree branches and bird feathers.
The Royal couple watched women competitors throwing the darts at a target, hoping to score a karey - or hit - before Kate had a go and nearly scored a direct hit on some female spectators.
Her first dart fell just short of one of them and when her second went wide, she felt compelled to apologise before suffering a fit of the giggles.
The display of sport came as the pair met King Jigme Khesar Namgyal Wangchuck and Queen Jetsun Pema on day five of their seven-day tour of Bhutan and India.
After being collected from the airport by the King's sister, all four took part in a spectacular ceremony at a 13th century royal fortress, featuring traditional dancers, flag-bearers, pipers, drummers and Buddhist monks.
The royal couples, who both have young children and are around the same age, then took part in the lighting of 1,000 butter candles - a ceremony that traditionally promotes wisdom and banishes darkness.
Bhutan, a nation of 800,000 people, is not part of the Commonwealth and there are no formal ties with the United Kingdom.
But a Kensington Palace source said the visit was requested by the Foreign Office to recognise Bhutan as a newly-emerging democracy that the UK is keen to support, in a strategically important part of the world.
The land-locked nation lies between China and India.
Bhutan's Prince Jigyel Ugyen Wangchuck said: "It is an historic visit. It not only links Bhutan and the United Kingdom as countries, but as people.
"Because the Duke and Duchess have such global support ... we feel that ... it will help Bhutan's image as well."
Kate, after arriving in a golden yellow outfit by Emilia Wickstead, wore a one-off Bhutanese-inspired outfit with a mauve and blue skirt made from local material and styled on the country's national dress for the ceremony, teamed with a top by US/UK-based fashion label Paul & Joe.
She later changed into a Tory Burch floral mesh full-length gown, ahead of dinner with the King and Queen.