I need to move my mother out of an assisted living residence that does not take Medicare to a facility that does. What is the process?

My understanding on this is that MediCare does not provide any long-term care assistance. If you need help, your parent needs to qualify for Medi-Cal (which may be referred to as Medicaid in other states).

I ran across an add before finding AgingCare.com for a free video on Medi-Cal funded dementia care - try nhscare The place is called "Nursing Home Solutions" ... I dunno if it will help, but they also have an 800 number: (800)773-6467. Can't hurt to request more information, right?
-FyreFly

Contact your local area agency on aging or medicare.gov. They have info and checklists you can print out for all the facilities in your area.
You may wish to check facilities that also take "medicaid" depending on her finances / eligibility.