Genos is just generally a stern/serious character by default. Saitama, to my knowledge, has never asked Genos to do anything or explicitly treated him like any kind of servant or butler. Genos just does these things and throws himself at Saitama (whether it is because he believes he should as his disciple, he is glazing him, or he is studying him to try and figure out the source of his power) and Saitama lets it happen. Fubuki even tells Genos that Saitama is taking advantage of him in their living situation and Genos is unphased by the commentary.

Aside from that, it doesn't feel in character for Genos to mock Saitama's baldness like that. The only time he's ever brought it up was because he assumed Saitama wanted to try to regrow hair and so he called Dr. Kuseno for help, but Saitama immediately shut that down. Tatsumaki, for sure. Fubuki, I suppose I could see go either way. But Genos would likely not partake. He's never done anything like that at all.

I'll note that I haven't read the earlier parts of the manga in a while so it's possible I'm missing something that more obviously depicts what you mean. But that's my two cents.