In a food processor fitted with an S-blade, pulse the dates until a thick paste forms.
Add the peanut butter and banana and pulse until thoroughly combined.
Add the oats and oat bran and pulse a few times until combined. The mixture will be very sticky. If it's too sticky to roll into balls, refrigerate for 1 hour or until firm enough to roll. If it's still sticky after refrigerating, use wet hands to roll the mixture into balls.
Roll into 20-24 1" balls. Chill the balls for 2 hours so that they can firm up. Refrigerate for up to 5 days and freeze any leftovers for up to 2 months.