Usually you don't have to bathe cats, unless they get into something icky or they have a condition like maybe your kitty has oily skin or something like that (hairless cats I think have to be bathed regularly, though). I agree that it's a good idea to look at what food he is eating to see if that's the cause. With Yuan because he has allergies, anything with fish makes him sick (he barfs and has diarrhea if he eats it), but there is something else that I haven't figured out exactly what it is that causes him to be itchy, and he starts scratching a lot and biting on and pulling out his fur and has watery eyes. So maybe your cat also has an allergy that makes his skin extra oily or something?
Does your kitty drink enough water? A lot of cats don't drink enough by themselves and so people either get them fountains (because that encourages some cats to drink more, like they like drinking out of the sink faucet), or they feed more wet food for the water content. That might be a reason too perhaps? Yuan drinks a lot and always has so it isn't a problem for him, but we live in a very dry climate so it probably makes him thirsty enough to drink.
Good luck to you and your kitty! He's very cute. <3
!LOLZ