Will I get bad credit if I don't pay for my mother's bills as her POA?

You have a power of attorney for your mother. You ask if you'll get a bad credit rating if you don't pat her medical bills.

Legally, an agent (or "attorney in fact") is not liable for bills of the person who gave him the power of attorney. So, as your mother's agent under a POA, you are not legally liable for your mother's medical bills.

However, I am not knowledgeable about credit ratings. It's my impression that credit-rating companies can decide pretty much anything they want about someone's credit rating, and that it is very hard to contest that rating. I have no idea if a credit-rating company could learn that you had a POA for your mother, or that (apparently) your mother had assets that you, as her agent, decided not to spend on her medical bills, or if that company would give you a bad credit rating because of that.