OP, I feel angry and violated on your behalf. Geezus some the thickos on this thread- unbelievable.
Yes, you made a mistake and quite frankly you need to get yourself better organised. Put the payment downstairs the night before, so you don't forget. The cleaner should never have to go without apayment.
However, you have established boundaries that she is not to go upstairs and she has crossed that. She has gone into your bedroom ( your private sanctuary ) disrespecting your right for privacy and then going through your handbag and purse. What if you didn't forget your handbag and purse. Would she have gone through draws and god knows what else onna money hunt?
All for all these posters assuming she catches the bus and has no money for the bus - based on what? How do you know the cleaner doesn't have a car? How do you know the cleaner didn't come from or was going onto another cash in the hand job? You don't! You don't know that she didn't have money? That perhaps she lives locally and could have come back later to collect payment if that hard up.
The OP has no indication she left anything on her note suggesting she was in desperate need of that money right there and then.
Quite frankly, she might have just thought it was okay to go through the OP's handbag and purse because in her mind she wasn't stealing and therefore didn't see it as being wrong ( screaming of chavy behaviour).
It's your call OP. I might feel sorry for her and not fire her ( well at least not immediately) but then feel paranoid leaving her in the house alone as she has proven she doesn't respect boundaries.