In BrE, we don't use "bills", we use "notes" for paper money. However, you don't need to use either. If you walked into any shop in the UK and said "I don't suppose/I'm just wondering if ... you can give me some change, can you?", they would know what you meant. Even better, specify the denomination of the note you want to change, for example "Can you change ten pounds for me?" It is possible that you might just want two five-pound notes, but usually the person in the shop will either say "No, sorry, I can't" or "Yes, how do you want it?" meaning "What combination of notes and/or coins would you like?"
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