Praise be to Allah.
If she can enter the bathroom in the house and heat the water, then it is not permissible for her to go to the public baths. Al-Tirmidhi (2801) narrated that the Prophet (peace and blessings of Allaah be upon him) said: “Whoever believes in Allaah and the Last Day, his wife should not enter the public baths.” Classed as hasan by al-Albaani in Saheeh al-Tirmidhi.
And al-Tirmidhi narrated that some women from Homs or Syria entered upon ‘Aa’ishah and she said: Are you the ones whose womenfolk go to the public baths? I heard the Messenger of Allaah (peace and blessings of Allaah be upon him) say: “There is no woman who takes off her garments anywhere but in the house of her husband, but she has torn the veil that is between her and her Lord.” Classed as saheeh by al-Albaani in Saheeh al-Tirmidhi.
But if she cannot bathe in the house, then it is permissible for her to go to the public baths as a matter of necessity, but she must be careful and keep herself covered.
Shaykh al-Islam [Ibn Taymiyah] said: The scholars said: A concession is granted to women allowing them to go to the public baths in cases of need just as it is granted to men, so long as they lower their gaze and guard their chastity. This also applies to women who are sick or bleeding following childbirth, or who have to do ghusl and cannot do it anywhere except in the public baths. End quote from Majmoo’ al-Fataawa (15/380).
He also said: As for women, they may enter (the public baths) in cases of necessity so long as they cover their ‘awrahs. End quote from Majmoo’ al-Fataawa (21/342).
And Allaah knows best.