@ysmina-- I'm not sure if this fits into the category of a spiritual bath but in Islam also, there is a requirement of washing before prayers (not a full bath) and also a requirement of a full bath or shower in certain circumstances.
For example, after sexual contact, a bath is due to become pure again. One cannot pray before having this bath and it is seen undesirable to walk around without being clean. The same goes for women when they finish their monthly period. It needs to be followed by a bath to be able to resume prayers.
While we wash or take bath, we can also say prayers for spiritual purification in addition to bodily purification. I, for example, always pray for God to "purify my soul as I am purifying my body."