Even if the horse has some bit-related trauma, that's not really an excuse. It doesn't matter why she behaved differently with her previous owners, all that matters is here and now with you.
Find a calm moment when you are in no hurry to ride. Put the bridle and the bit on her. Doesn't matter how much it takes, just try and be gentle about it. When she finally accepts the bit, praise her a lot, give her food treats if you use that, click if you use the clicker, make sure she understands that you are happy with her.
Then, remove the bridle and put it on again. If it takes another 20 minutes, that's ok. Put the bit on and off again and again, she'll relax sooner or later.
Repeat the lesson on different days until she is cool with you bridling her, and repeat it again if after some time of "good" bridling she shows reluctance again.
There's nothing wrong with using whatever bitless option you like, but I think that it's better if you are able to put the bit on her. Then you can use or not use it, but using a bitless because you can't put the bit on is just wrong; it's a wrong start for her and for you, because it means that she's training you to do what she wishes.
You should tell her that she's not having her way. Ok, being calm and gentle, without violence and all. But in the and it's going to be your way.