If I'm not mistaken we refer to such a person as a "talmid chaver" -- I was Rabbi ABC's student, but now I've learned enough to be his colleague. It appears that some respect is still called-for.
Shulchan Aruch YD242:4 (among other places) discusses the concept. For instance:
One may not render psak in one's rebbi's presence ... however if one is 10 miles [or more] away from his rebbi and on rare occasion he was asked on a halachic matter he may answer; but to establish himself as a decisor and sit and rule on a regular basis -- even halfway around the world from his rebbi -- is prohibited unless his rebbi has died, or has given him permission to do so. ... [On the other hand,] a talmid chaver is prohibited [to render psak without permission] in a ten-mile radius, but outside of that is permitted.
[When permission is needed from a rebbi], even if one received permission from one rebbi, he must receive permission from all his "true rebbis." Rama comments: "true rebbi" here doesn't mean "learned the majority of your wisdom from him" as there can only be one of those; rather, "true rebbi" as opposed to a talmid chaver, i.e. someone who grew in Torah and became a colleague to his rebbi, nearly as great as him.
It's discussed further in Bava Basra 158b; Be'er Heiteiv YD242.9 quotes Maharik who points out, for instance, that the majority of Reish Lakish's torah learning (as well as his ordination) came from Rabbi Yochanan, yet Reish Lakish grew to the point where he was able to rule differently in Rabbi Yochanan's presence.
The whole bathhouse thing (see Rama, by the way, only an issue if everyone's naked. If you have underwear this doesn't apply) is limited to a rebbi muvhak, someone from whom you've learned a majority of your wisdom. Firstly those are rare today, and what's more it would sound from the language of shulchan aruch that talmid chaver and rabo muvhak are mutually exclusive concepts.
It's said that the Vilna Gaon's alef-bet teacher once visited Vilna and was given an extremely warm and reverential welcome. At which point the Vilna Gaon's first Gemara teacher tried visiting and was treated politely but not much more. "My first teacher taught me alef-bet and that's served me well my whole life; but the Gemara that you taught me, I had to reteach myself in a whole different way", said the Gaon. (Or something to that effect.)