You could translate "The woman is worried about the bill" quite literally into "Kobieta martwi się o rachunek" though.
Not exactly. In Polish we we use different constructions when talking about the object of our worries or about the cause of the worries.
1. Martwię się o Tomka, bo jest chory = I'm worried about Tomek because he's ill
2. Martwię się chorobą Tomka = I'm worried about Timek's illness
The these examples Tomek is the object of my worries, while the illness is cause of my worries.
So in your example "Kobieta martwi się o rachunek" means that the woman is worried about something "unpleasant that happened/will happen to the bill" - which doesn't make much sense...