The celebrity news Web site TMZ said Friday the former Skid Row front man and Bierk have been separated since April. They have three children together.
"We have tried to work things out for the sake of our family but it has become apparent that our differences at this point are irreconcilable," Bach told TMZ. "In 2011, we go our separate ways."
Bach, 42, was arrested last month for allegedly biting a bartender during a brawl in a bar in Ontario. He was charged with assault, possession of marijuana and mischief.