Ok really, whats the plan here. Because now the prince knows he was lied to. He wont side with the bishop, he will out them. The only troops loyal to the bishop are down. Even if the bishop kills her the truth is widespread and multiple armies will be after them.
This battle was already a total loss for them, they should have just fled and silenced the prince. Or better yet just silenced him before the deception became known. Might have been able to play off that they were deceived.
But this... there just no building on this. Not without the prince siding with them, and without enough forces. Unless they still plan to flee, but they are out of forces to kill the prince and other witnesses.