Here is a composition by Shri Kanakadasaru. Shri dasaru says, people taking the bath by dipping the body in water is not a bath.
One should have good character; not thinking of bad to anybody is also a bath and many more actions like that. It is real bath.

Lyric follows:

rAga: haMsanAda
tALa: Adi
rachane: shrI kanakadAsaru

snAnava mADiro j~jAna tIrthadalli
mAnavarellaru maunadoLage niMdu /pa/

tanna tAnaritukoMbude oMdu snAna
anyAyava mADadiddare oMdu snAna
annadAnava mADuvudu oMdu snAna
hariya dhyAnave adu gaMgA snAna /1/

parasatiya bayasadiddare oMdu snAna
paraniMdeya mADadiddare oMdu snAna
pararige upakAra mADuvudu oMdu snAna
paratatva aritukoMbudu oMdu snAna /2/

sAdhu sajjanara saMghave oMdu snAna
bhEda bhAvavanu aLidoDe oMdu snAna
AdimUruti kAgineleyAdi kEshavana
pAda dhyAnave adu gaMgA snAna /3/

Meaning of the song:

You people take a bath (snAnava mADiro)
with the water of knowledge (j~jAna tIrthadalli)
All human beings (mAnavarellaru)
stand in silent (maunadoLage niMdu)

If you know yourself (tanna tAnaritukoMbude) - it is one bath (oMdu snAna)
One bath - is common to all
If you have not any unjustice (anyAyava mADadiddare)
If you donate some food (annadAnava mADuvudu)
Remembering HARI (hariya dhyAnave) is a
great bath in water of Ganga river (adu gaMgA snAna)

If you are not after somebody's wife (parasatiya bayasadiddare)
Not blaming others (paraniMdeya mADadiddare)
Helping others (pararige upakAra mADuvudu)
Knowing (aritukoMbudu) the supreme truth (paratatva)

Having company of good people (sAdhu sajjanara saMghave)
Not discriminating others (bhEdabhAvava aLidoDe)
Surrending at the feet of Supreme (pAda dhyAnave)
Kaginele Adikeshava and knowing HIM (kAginele AdikEshavana)
is the great bath in Ganga river (adu gaMgA snAna)

Listen to the song here: No details of singer available.
Spoiler: