burning bear: i.e., the constellation Ursa Major. "Ursa Major" is Latin for "Big Bear." Ursa Major circles closely about the north star (the pole star). Hence in the next line stars of the Ursa Major are referred to as "guards of th' ever-fixed pole," probably the two stars in the Big Dipper which are in line with the pole star.
Image Source: tpwd.texas.gov |