You can pay her bills and get her to reimburse you. If she will be incapacitated for a while and you do not have her power of attorney, you may need to seek a guardianship over her.
What Mr. Early said is entirely correct. You do not incur any debt yourself by making the payments for her during her hospitalization. If you cannot make them, talk to a probate attorney about a guardianship in order to access any funds she may have, but know that it will be monitored by the Court and any of her funds spent MUST be used for her benefit.
You can always pay someone else's bills and not take on personal liability for them (or anything else). The question is can (or will) you be reimbursed for doing so? If you are not worried about that, then go ahead and pay them and address reimbursement later. You do not mention whether or not she signed a financial power of attorney. If so, the POA can pay her bills using her funds, as provided in the document. If not, then you need to see how long she may be incapacitated. If it will be for a short period of time, you can address getting a POA in place for the future when she is able to understand what she is signing. If she does not recover soon (or will be incapacitated for a long time or indefinitely), then you (or someone else) will need to file a guardianship, so there will be a guardian to take care of her and her financial obligations. You should contact a good probate attorney to go over the other important facts, issues, and documents you have to develop a strategy going forward.
Mr. Arenstein's answers are not intended to create an attorney-client relationship and are based only on the limited information provided in the question. Thus, his comments should not be considered legal advice, and persons seeking legal advice should contact Mr. Arenstein directly and/or another attorney with a law license in the state in which the situation arose. Mr. Arenstein is licensed to practice law in Ohio and the United States Tax Court.