Is it permissible for a woman to bathe her elderly father taking into account that he is able to move? [What is the ruling on this?]

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.

Yes, it is permissible for a woman to bathe her elderly father if the father is covered between his navel and the knee but it is not permissible for her to touch what is between his navel and knee, as this is the 'Awrah (parts of the body that must be covered in Islam) of a man. Since it is not permissible for her to look at this part of the body, it is not permissible for her to touch it.

Allaah Knows best.