I use a Pelham works great
Train the horse to soften don't get a harsher bit.
I use a kimberwick on my strong headed quarter horse, it seems to have helped a lot
Why is she strong? Is she in pain? Confused? Hard mouthed? Actually ignoring you? That's the first thing to look at. If you determine she's ignoring you, then I would try a pelham or some sort of kimberwick.
Going back to ground work to gain her respect and get her listening would also probably be a good idea. Stepping up the bit is a bandaid, not a fix. I used to have a really hard-mouthed gelding who was used as a lesson horse before I got him. I worked with him on vocal cues- "whoa" and "easy"- in hand and on the lunge line before I started riding him again, and we eventually got to the point I was riding him in a broken kimberwick and he was slowing when I just closed my fingers.
It all depends on the horse. I'd say a rubber two ring is pretty versatile:)