For the purpose of cleansing the body, the recommended ingredients are water and earth (mud or soil). So, for bathing, only water is recommended.
Manu Smriti 5.134. In order to cleanse (the organs) by which urine and faeces are ejected, earth and water must be used, as they may be required,
likewise in removing the (remaining ones among) twelve impurities of
5.135. Oily exudations, semen, blood, (the fatty substance of the) brain, urine, faeces, the mucus of the nose, ear-wax, phlegm, tears,
the rheum of the eyes, and sweat are the twelve impurities of human
5.136. He who desires to be pure, must clean the organ by one (application of) earth, the anus by (applying earth) three (times),
the (left) hand alone by (applying it) ten (times), and both (hands)
by (applying it) seven (times).
Also, see the following verse:
5.109. The body is cleansed by water, the internal organ is purified by truthfulness, the individual soul by sacred learning and
austerities, the intellect by (true) knowledge.