Could your bird live in your bedroom so the cats have the rest of the house and when you want the bird out in the rest of the house lock the cats up for a little while? Its not whether she is used to them that's the issue, its that she is prey and they are predators and terrible things happen. Just the other day another bird on the forum lost its life to a pet cat.
I'm sure you love her but to ensure her safety a bit of restructuring might be required.