When does she eat?
Does she come in for an evening meal?
If so that would be the time to shut the flap once she has come in.
It hard to tell with someone elses cat how it will react but Sasa will run away if the flap is shut to her and she broke through it after about 3 months cos I shut her in at night.
Now I cant touch Sasa cos she is so scared and she will get terrified if a door is shut on her, so I would never shut her in. However she loves her creature conforts and comes in at night, and most of day now as long as she can go out when she needs.
If Bronte comes when you call her you may have set a pattern and need to start calling her earlier as tha nights are drawing in.
Does she like treats, if so you could try seeing if she will react to a box of them being shaken or a dish being banged, anything to use as a calling in signal.