I’m afraid you can never put a female piggy in the same cage as two boars - it will cause huge problems including pregnancy.
In fact when you have two boys you can never add another piggy at all (of either sex).
It’s also not recommended to bring a female piggy even into the same room as bonded boars as if two boars even smell a female then the boys can start fight with each other and break their bond.
He is biting the bars because he is now desperate to get to her - which he must never do.
Please keep the two boys together, provided they are still happy to remain together (adding the female can ruin the boys bond).
If the boys bond has been affected by the presence of the female, then they may also start to fight and fall out (hopefully they won’t but it is a risk now they’re in the presence of a female). If this happens then sadly the two boys will also have to be separated and live in separate cages
Please keep the female in a separate cage by herself and well away from your boys - ideally she now needs to be kept in a separate room so the boys cannot smell her.
You will need to get your female her own new female friend to live with.
You must make sure you bond your female and her new friend properly following neutral territory processes. This is the guide for how to bond her with another female
Bonding and Interaction: Illustrated social behaviours and bonding dynamics
How long was she in the same cage as the boys?
(there would now be concerns she could become pregnant)
As I mentioned above, as you have a bonded pair of boys, you can not add any other piggies in the same cage with them - two boys need to remain just the two of them at all times.
Even if the new piggy you bought home was another male, you would still not have been able to add him into the cage with your current two boys. Trying to keep three boys together does not work and would also cause your boys to fight and fall out. Boars need to be kept in pairs only
Adding More Guinea Pigs Or Merging Pairs – What Works And What Not?