Until her assets are nearly used up, she is considered private pay. Medicare Part A doesn't likely have a premium, but Medicare Part B and any supplemental policies (these cover doctor visits, etc. while Part A is more for hospitalization) carry a premium. Until any of us have used up most of our money, including savings, we pay these premiums and co-pays, plus a separate Medicare Part D policy for drugs (if we choose). Once most of the assets are gone, then people can qualify for Medicaid, which is for the poor and won't carry premiums.
I know, it's hard. I've been there.
Carol