"One does not play with bears."
Translation:Man leker ikke med bjørner.
"Spiller" is used in relation to games and musical instruments, so it's a less likely candidate here.
However, should you ever feel the need to warn somebody not to play chess or in a brass band with bears, then it would indeed be the correct word to use.
That's the definite singular form ("the bear"). Here, you want the indefinite plural, "bjørner".