Art Young is generally credited with being the first modern man to take a grizzy and polar bear with a bow.
Chester Stevenson, well after the event, wrote an article on the taking of, what he described as a grizzly in 1911 in Oregon.
Ralph Whaley, a relatively unknown archer born in 1888 gave an account of taking a polar bear [no gun, no backup, only his bow] and claimed to have taken most North American game with a bow. All this was recorded in a series of interviews by an outdoor writer and acquaintance. Whaley never wrote of nor sought publicity, and might very well be one of the greatest unknown bowhunters from the early days. After years of searching for information on Whaley, by a stroke of luck, I located the author of an obscure article on him. I've since purchased the rights to his original article, the complete interview, notes and other unpublished information.
Not to take anything away from Young, but if one considers the above to be true, then Chester Stevenson might be the first modern archer to have taken a grizzly and Ralph Whaley might be the first to have taken a Polar bear. Then again, there "might" be others from the past that may have been their earlier.