Do Advaitin Sannyasis who have renounced rituals bathe daily?
In the Sannyasa Upanishads various kinds of Sannyasis are mentioned viz - Kuticaka, Bahuduka, Avadoota, Hamsa, Paramhamsa.
Among these, only for the Parmahamsa Sannyasis bathing is not ordained. Others must bath. Avadootas and Turiyatitas, however, are required to take wind and ashes bath respectively.
"A celibate Kuticaka should give up his family, put away his bowl, discard his water strainer, throw away his staffs, and forsake the heavenly worlds." So said Prajapati.
"Thereafter let him function without mantras. He should bathe at the start of the three junctures of the day, and, in deep contemplation, he should realize his union with the Self.
A pot, a drinking cup, a sling, a tripod, a pair of shoes, a patched garment against the cold, a loincloth, a water strainer, a bathing cloth, and an outer garment: an ascetic should avoid anything else other than these.
Let him sleep on a river bank or in a temple. Let him not afflict his body with extremes of pleasure or of pain. Let him bathe, drink, and cleanse himself with water that is purified. When he is praised let him not rejoice, nor curse others when he is reviled.
Laghu Sannyasa Upanishad
"A bath is ordained three time a day for hermits and Bahudakas, and just once a day for Hamsas. There is no such rule for Paramahamsas.
"Silence, yogic posture, meditation, patience, solitude, desirelessness, and equanimity: these seven are practiced by single staffed ascetics
Narada Parivrajaka Upanishad
"He shall avoid speaking or chatting with women, looking at them, dancing, singing, or laughing with them, and reproaching them.
"Bathing, muttering prayers, divine worship, sacrifices, propitiatory rites, and rites such as the fire sacrifice do not apply to him, O Narada, in this world.
"Neither do divine praise, rites for ancestors, pilgrimages, vows, categories such as right and wrong, injunctions, and temporal activities.
Narada Parivrajaka Upanishad Chapter 6
"A bath is ordained three times a day for Kuticakas, twice a day for Bahudakas, and once a day for Hamsas. A mental bath is ordained for Paramahamsas, a bath with ashes for Turiyatitas, and a wind bath for Avadhutas.
A vertical mark on the forehead is ordained for Kutlcakas, a triple horizontal mark for Bahudakas, both a vertical and a triple horizontal mark for Hamsas , the smearing with ashes for Paramahamsas, a spot with sandal paste for Turiyatitas, but none at all for Avadhutas.
Narada Parivrajaka Chapter 7
Now, we just need to find out to which of the aforementioned groups the "Adavaitin Sannyasis" belong. By going through their Wiki page I found out that they carry a single staff and which is a feature of the Hamsas.
Bahudakas are those who carry a triple staff, a water pot, a sling , a shoulder yoke, a water strainer, a bowl, shoes, and a seat; who wear a topknot, a sacrificial string, a loincloth, and an ochre garment; who beg their food from virtuous Brahmin households; and who thus seek the self
Hamsas are those who carry a single staff; who wear a sacrificial string but not a topknot; who carry in their hand a sling and a water pot; who spend only one night in a village and five nights in a town or a sacred bathing place; who perform penances such as the one- and two-day fasts, the krcchra, and the lunar fast; and who thus seek the self.
Paramahamsas are those who carry no staff; who are shaven-headed; who wear a loincloth and a patched garment; whose emblem and conduct are concealed
So, they should bath as prescribed for the Hamsas (i.e. once a day). As, they carry a single staff, they are not Paramahamsas (for whom bathing is not ordained).