Playing a friendly game the other night, and one of the table was playing the Veloci-ramp-tor deck. He plays Bronzebeak Forager which states that when it enters the battlefield you may exile a target none land permanent until Bronzebeak leaves the battlefield. It also allows you to pay X/W mana equivalent to the exiled creatures toughness to send the exiled card to the opponents graveyard in return for life.

They exile my commander, and the table is split as to whether the commander remains in exile until Bronzebeak leaves the field OR the ability is used that sends it to the graveyard. Or does the commander immediately return to the command zone with an increased mana cost?

I'm sure someone must know the correct answer, thanks in advance :)