Is there any textual evidence(in Hindu scriptures) to bath with clothes only? Or it is the rule added according to time?
There is textual evidence.
Manu Smriti,Chapter 4 Verse 45:
4.45. Let him not eat, dressed with one garment only; let him not bathe naked; let him not void urine on a road, on ashes, or in a
cow-pen,(Na Nagnah Snanam Aachareth)
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Here him refers to a Brahamana(or to a Snataka ),but in general it will be a improper conduct for other persons(householders for example) as well, because while God Varuna is making us pure,by his grace, we are not showing him due respect, in turn, if bathing naked.
Edit-I have searched the Parashara Smriti.Unable to find any prohibitions regarding bathing naked in it.
Thus we have prohibitions in Manu Smriti but nothing in Parashara & among which the later is supposedly more precisely applicable in Kali Yuga.
We can interpret these findings in two ways:
1)Since Parshara does not mention anything we need not worry about it because had it been important would have been contained in that Smriti.
2)Manu Smriti condemns bathing naked and Parashara Smriti does not contradict it.So,we can assume that,in this particular case, the laws of Manu are valid in Kali as well.
Update-"Some articles says that, since there are no personal bathrooms in old times, people use to bath with clothes."-- This is not true.I have found evidence that bathing nude is improper conduct even if one is bathing in a closed place.
Maharishi Vyasa describes about "saadaacharaa"(right or proper conduct) in this chapter of the Brahma Purana .He says:
Grihastena Sadaakaarya maachaara pari-rakshanam,
Nahyaachaara viheenasya bhadramatra paratravaa,
Yagna daana tapaaseeha Purushasya na bhuyatey,
Bhavanti yah sadaachaaram samullanghya pravartatey/
Grihastaas or family-persons ought to observe and protect Sadaachaara
Pravartana as those without it would neither have ‘Iham’ / the
contentment of current life or ‘Param’of post-life; to those who
neglect the principles of Sadaachaara are not eligible to the fruits
of Yagna- Daana-Tapas
Then he gives a long list of such proper conducts or sadaachaaraa.And in that list we find:
Men and women of virtue should.......never bathe or sleep in nudity
even in closed places......