The older Bears are easily identified by the decals or silkscreens on the limbs. Those marked Grayling, Michigan are old (1947-1977) and the newer models will have the Gainesville, Florida markings. Serial numbers may be helpful, but they are not a reliable indicator of year made.
Keep in mind that Bear implemented yearly changes, cosmetic and otherwise, but most of us love the Grayling models primarily for how they shoot, how they look...and nostalia.
For beauty's sake, none have exceeded the Bears from '57-'77 models.