Originally Posted by Eldest
Try having the familiar change into a animal companion when they take their first level of druid. It would be a bit weird (your pet owl just turned into a bear) but it solves that problem.
"OWL IS EVOLVING! OWL EVOLVED INTO BEAR!"
Whatever floats your boat. My opinion is there is no right answer here. It's really dependent on what the DM thinks is appropriate for the setting.
Edit: Hint: Owl's final form is Owlbear