Unfortunately for you, what you were told by the county court is correct. Since you do not have a written agreement with your roommate, she is considered a month-to-month tenant. You are her landlord. Per GA Law, the landlord must give a month-to-month tenant 60-days advance notice of a demand for possession. And any tenant must be formally/legally evicted if they fail to leave after the time granted in the demand. The good news is that she is still responsible for paying rent during those 60 days; and you can add any unpaid rent to your eviction action. (If she leaves without you having to evict her, you would still be entitled to file a complaint against her for any unpaid rent.)
~ Kem Eyo
The above answer is a general explanation of legal rights and procedures. It does not constitute legal advice. Nor does it establish an attorney-client relationship between the individual posting the question and the attorney providing the answer.