If my mother does not have a Will but has set me up as the beneficiary on her bank accounts, will I need to go to court or involve a lawyer to pay some of her final bills?

If you are the beneficiary on a "pay on death" (POD) or "transfer on death" (TOD) account, the account balance will be paid to you upon your mother's death.  You will not need to go to court or hire a lawyer to receive the balance.

You are not necessarily responsible for your mother's bills after she passes away.  In many states, POD and TOD accounts pass outside the estate and are not subject to creditors' claims.  After your mother passes, I would accept the balances from her accounts, deposit them into my own account, and wait to see what bills exist.  If they are significant, you can consult a probate attorney in your mother's area to see if you are responsible for any of them.