Could a free woman travel unescorted? Certainly she could.
It’s just that it would be extremely unwise for her to do so.
"You are certain that you are a free woman?" asked the man.
"Yes," I said.
"Where is your escort, your guards?" he asked.
"I was traveling alone," I said.
"That is unusual for a free woman," he said.
I was silent.
Kajira of Gor    Book 19    Page 214
And, too, the free woman, to her chagrin, can recall the incipient feelings in her body, and her gasping, and how her small arms touched, and then held, and then clutched, gratefully, the body in whose power she lay. How they had laughed, when a spasm, to her shame, had rocked her. Then, having been given a taste, however brief, of what it might be to be subject to the mastery, she was returned to freedom, to live as she could, the life of a free woman. Such a woman, commonly, in her misery and loneliness, in her shame and humiliation, in her uncertainty and confusion, begins to roam the high bridges, frequent lonely streets, and wander unescorted outside the city gates. She courts the collar. She seeks it. She beseeches it. She weeps with rapture as she is stripped and bound.
Mariners of Gor    Book 30    Page 324
At gambling houses, unlike taverns, free women, if escorted, were welcome. Might not they be parted from their money as well as their male counterparts? There is little economic point in neglecting possible sources of revenue. At the opposite wall, there were some curtained thresholds behind which slaves might be kept. These were not permitted on the floor during business hours, in deference to free women.
Avengers of Gor    Book 36    Page 176