When the hell did the Chinese choose bows over guns?
Handgonnes were produced in very large numbers in the Early Ming Dynasty and special military divisions called "Shen Ji Ying" consisted entirely of firearms wielding troops. The Matchlock arquebus were introduced in the mid-1550s and were commonly fielded in Southern China.
Even the Manchus, who were notorious for their archery skills, fielded large numbers of musketeers during the late 17th century till the 18th century. Although the guns fielded by the Chinese were technologically inferior to their European and American counterparts they were still, as a matter of fact, guns, not bows
It is my impression that the Ming made more extensive use of firearms and guns than the Qing. I believe that guns were not favored by the Qing for the following reasons-
1) The Manchus were an ethnic and cultural minority which ruled over a much, much larger Han majority. They wanted to have a monopoly on military power. The Manchu military relied on highly skilled horseman and bowmen as the decisive factor on the battlefield; they did not want to proliferate a weapon that would allow Chinese peasants to challenge their bannermen. It can be seen by the Muslim, Nien, and Taiping Rebellions in the 19th century that even Chinese peasants with limited access to firearms can prove to be a serious threat to Manchu military forces, caused massive damage over very large areas, and took years to contain. In fact, during the beginning of the Taiping Rebellion, the Manchu bannermen were
wholly ineffective against the Taiping Rebels, which relied heavily on firearms. It is interesting to note that the Manchus did make wide use of cannons and several other larger types of firearms, since these weapons were more difficult to make, thus allowing the Qing rulers to maintain a monopoly on the production and distribution of such weapons. It is a lot more difficult for peasants to produce cannons in backyard workshops.
2) The Manchu military's primary role was to maintain control within the Empire, not to fend of external threats. Apart from several campaigns against the Mongols and Tibetans, and a few minor clashes with the Russians, the Manchus never faced any real external threats. Their military was primarily tasked with preventing and putting down rebellions in China, Vietnam, and other areas of the empire. They did not need guns to defeat armies of discontent peasants. This is in contrast to the Ming military, which faced constant threats from the Mongols, Manchus, and Japanese.
3) A very important aspect of traditional Manchu culture was martial prowess, specifically archery and horsemanship. Even into the late 19th century, during the yearly military examinations, which ran parallel to the civil examinations, candidates for military positions were tested on their skill with the bow and on the horse. In Europe, as firearms proliferated, the status and position of the knights and nobility were called into question, and European society came to be dominated by the merchant class. The Manchu upper class wanted to maintain their status in Chinese society and did not want the legitimacy of their position questioned.