Can a true Sikh bath completely naked or does he/she have to have the five K’s tied with him/her while bathing?

In older times people used to bathe in rivers, public wells, or sarovars. Even the bathing places at ‘kaccha houses’ used to be in open. Hence, most Jathebandis included instruction of wearing kachhehra and 5Ks at all times including bathing. It must be noted that such instructions were very correct considering the social factors of those times.
Bathing in a private bathroom with a lock from inside is a very recent development.
Another example: Removing the kirpan while onboarding an international flight is also a recent development. Such scenarios were not present in earlier days.
Hence how you bathe privately is completely a personal choice. The earlier decision of keeping 5Ks at all times was also as per considering societal factors. Now removing kirpan while on flight or without-kachhehra while bathing in private is also correct considering societal factors. Neither the earlier restrictions were Gurbani perspective, nor the recent relaxations are against Gurbani. Thanks.