You might have something there, maybe the Warden has an inkling as to what the swords can do and wants to force Bern into a position where she -must- block or Polly gets squished? Would also be a situation where Bern could discover what the swords do together as a pair.
My theory is that the Warden recognised Bernadettes ability, but also her weakness: Innocence.
Bernadette lives the live of a fighter, but has found a way to maintain her innocence in it. She has a code that goes way beyond a usual Knight's Code of Honor, she is basically a pacifist with swords.
Her entire fighting technique reflects that. Be passive. Be evasive. Do not risk. Do not become guilty.
But if you are against a foe you cannot win othervise, you must risk. You must seize a moment. In the right moment, in that split second, you do not need to be innocent, passive, concerned, you must act, dash forward, take the price. Shut out the thoughts and the concerns, shut out passivity. It is impossible for Bernadette to do that, she rests in herself - this is good, but not for a fighter.
But as I said it goes beyond this: with her style Bernadette also does not risk to become "guilty" in any way. She does not risk having to kill a feo. She fights, but the killing? That do others, people who fight with her and are more rash. She does not risk doing something morally questionable, does the other person deserve death, no matter this fight? Maybe, maybe not. Bernadette has no problem, she stays back.
To use something visual: In her profession she might get literally her hands bloody but her whole fighting style is there to minimise the chance to metaphorically get her hands bloody (funny inversion of how it usually goes).
If Bernadette wants to unlock her maximum potential - and thus her ability to survive as much as she can; something she needs here in this arena - she somehow has to lose a part of that innocence. She has to understand she won't make it with her full conscience intact, that while she is a good person, she has to do bad things if her profession is a fighter and if she wants to survive.
Warden offers her that before she puts her in a fight where she a) needs to use it for b) the price to have a perspective to get out of the arena.
Polly takes away all offers from Warden. The offers all have one thing in common (as was pointed out already): they make Bernadette suffer through unfair hardship without killing her. In short: They take a part of innocence and leave a black mark where it was, so Bernadette must come to peace with that black mark. This can then fuel the power she needs for her
chosen profession.
Polly gets Bernadette into the arena without all that.
What is left here where Bernadette can "suffer, but not death. Lose something that leaves a black mark on her soul". There is only one thing left. Polly.
I think this is at least what Warden thinks and I find it possible that when Warden starts talking next she will make Polly understand, which leads to Polly "doing all she has to do protect Bernadette". She'll dash in a sacrifice herself. Being killed in those cirumstances? Yes, totally is on par with the options that were offered to Bernadette.