Kyudo (弓道) This kanji for do was used by the early buddhist priests in Japan to denote a way, not just any way... but a way to enlightenment.
This 'do' is the Japanese pronunciation of the Chinese Tao, and thus denotes a way to balance, blend, and merge the shadows and sunshines of life into one... or not exactly one... but not two either... Well that's Zen...
Buddhism was developed from Yogic Hindi Practices in India... When Buddhism traveled to China, at one point it merged with Taoist Principles; Chinese Chan was born as one of their offspring. When Chan arrived in Japan, and again mixed and merged with what was there; it became Zen. Now it has arrived in the West and will emerge anew once more...
Taoism and thus the Do of Japanese arts was developed in Japan as Zen. Zen is thus Do and Do is Zen.
Did you know that the kanji we use in Buddhism for the Buddha is a man standing with a bow and two arrows?
There have always been shamanistic uses for the bow in Japan; One of Japans' earliest written records in Japan, The Kojiki, refers to these rituals with these same kanji, but was usually said as Yumi no Michi 'The Way of the Bow;' they used the bow primarily as a way of purification.
Most who owned a bow were warriors and did kyujitsu not kyudo. Though I'm sure some did both; similar to those like the Ogasawara Family who developed ceremonies and rituals for the bow. Plus there were some schools of Zen that used the bow as a Do, as well. But the bulk of those with bows were warriors doing kyujitsu.
To my knowledge the first to publicly publish and promote his whole school as KyuDo rather than KyuJitsu was Master Morikawa Kozan of Yamato-ryu in the 17th Century. By doing so he began the process that continues today, of moving the use of the bow as A Way; no longer just for killing or technical sport, but for 'something' else. The something else may depend on who's holding the bow. Zen? Well the 'Do' really denotes Zen, since that is how the Taoist principles most heavily flowed into Japan; the terms are almost used interchangeably in some Zen schools. But I think today the term Do has often come to mean simply something other than jitsu, or to separate the modern form from the older koryu.
In the Artistic Ways of Geido like Calligraphy, Tea Ceremony and Flower Arrangement they most often readily accept and promote their Zen roots; but the warrior class was just as likely to embrace Confucian Values as well as Zen and mixed and matched them to their liking; so the Do in BuDo like KyuDo can be Zen, or Confucian, or secular, or Sport; it most likely just depends on who runs any particular school and where they find their own roots. Some teachers who know Zen may use it, but others may use Golf, or whatever they or their students know to get the principles of Do across. Whether or not we call it Zen, now it's Do. So, we call it that... KyuDo, 'The Way of the Bow'.