If the word is "intetkøn" (neuter gender) it's -erne and if it's "fælleskøn" (common gender) it's -ene. "Bjørnene" is common gender because you say "en bjørn" and not "et bjørn". the word "en" indicates that the word is common gender and the word "et" indicates that the word is neuter gender. The same goes for the -er and -e in indefinite plural, where -er is used on neuter gender and -e is used on common gender
This is not correct as for instance en mappe becomes mapperne in the plural definite, and as Lena2492 pointed out en pige becomes pigerne.
The catch is to look at the last letter of the noun. In general nouns that end with a vowel get -r or -er in the plural and -erne in the plural definite. Nouns that end on a consonant generally get -e in the plural and -ene in the plural definite.
Keep in mind that some nouns are irregular and do not follow this pattern. For instance en sko becomes sko in the plural and skoene in the plural definite.
From the Tips and Notes of the Plurals skill:
„Whether a word uses -er or -e is unrelated to its grammatical gender, and is something that must be learned by heart. Furthermore, some nouns do not change at all in the plural. These must also be learned by heart. There are, however, some general guidelines:
• The -er postfix is the most common one.
• Nouns containing multiple syllables usually take the -er ending.
• Single syllabic words of the common gender (n-words) often use the -e ending.
• Short, single syllabic nouns of the neuter gender are most likely to remain unchanged in the plural."