According to Landis in Twenty-Two Caliber Varmint Rifles the 218 Bee is basically the .22 Koshollek. He has this to say:
"The primary reason for the .218 Bee is to provide a high-speed load in .22 caliber, with a 300-yard trajectory about that of the .30-1906 service charge, which can be used in a short-receiver type, lever action rifle which can be carried conveniently in scabbard, on the back seat or the floor of an auto, a farm wagon or a sled, uses light recoil and moderately inexpensive ammunition suitable for the use of cowboys, shepherders, and ranchers needing a hunting rifle with light weight but reasonably powerful ammunition and which will cover the varmint and game field up to and including an occasional shot at deer or coyotes. Or, in the East, at woodchucks."