Packlord Archetype.
Instead of having one bear companion, have one unadvanced bear per class level. Now give your cohort this archetype. They also have one bear per class level. Then the both of you take Additional Animal Companion as often as possible. This will give you (class level -3) bears each time you take it. (Or one bear that can actually get animal companion bonuses, if your DM is dealing with too many bears.)
At level 7, you'll have 2 Druid-bears, 7 primary bear companions from Packlord, 5 Cohort primary bear companions, 4 bear companions from Additional Animal Companion, and 2 bears from your cohort's Additional Animal Companion. That's 18 bears. (Or 14 if Additional Animal Companion only gets you one companion)
At level 9, when you have your Cohort take Leadership, you'll have 3 Druid-bears, 9 primary bears, 7 cohort' primary bears, 5 cohort'' primary bears, 12 bears from 2 Additional Animal Companions, 4 from cohort' Additional Animal Companion, and 2 from cohort'' additional animal companions. That's 42 bears. (Or 28 if Additional Animal Companion gets you only one companion.)
At level 11, when Cohort'' takes leadership... you'll be up to 78 bears total, or 43 if Additional Animal Companion sticks to one animal companion.
And then you get into summons and bears you diplomance into joining your horde, and you realize your DM has already flipped the table and left.
EDIT: If you want to have Natural Spell, that shrinks the number of bears a decent amount; at level 7, it's down to 12 bears; at 9, 30 or 25; at 11, 54 or 44.