The clearest answers are 'Yes, please' or 'No, thank you'. If you say simply 'Please' or 'Thank you' on its own, in a positive tone, it would be taken as a 'Yes'. You can say 'I'm fine, thanks', for example, or 'I'm OK, thanks' or 'I'm all right, thanks', and this would be understood as a polite refusal. Any of these would mean that you don't need a bag. 'That's fine' may confuse the listener. If I were the cashier and someone replied 'That's fine', I wouldn't be sure whether they were accepting or refusing. It may not be clear what 'That' referred to, or why it was 'fine'. Remember that most of our communications in these circumstances are non-verbal. Body language, facial expression, manner and tone of voice are often more important than what we actually say. If the supermarket is noisy, the cashier may not even hear what you say, but will pick up on non-verbal clues. For example, if you say 'That's fine' in a positive, expectant way, with a hand held out for the bag, the cashier will take your response as a 'yes'. If you say it in a dismissive way, look away and carry on picking up your purchases, he/she will take it as a 'no'.

You're correct. If you wanted a bag, you could say "yes I would" "yes, please," "thank you," or "sure."

I'm fine . Thank you ( you dont want ) Yes , please ( if you dont mind ) - you want a bag