It may also be a matter of personal preference. To me, "I am bathing" and "I am washing" sound too much like a D.H.Lawrence (1885 - 1930) novel. I do not much occasion to say this kind of thing because when I am taking a bath or a shower I do not answer the telephone or the doorbell. If ever I do need to say these things, I prefer saying "I am in the shower" and "I am taking a bath." The human mind is so strange. Your question reminds me first of D.H. Lawrence and then, as I am writing now, of that famous photograph of Princess Margaret in a bathtub filled with water (presumably at Kensington Palace) wearing the celebrated Poltimore tiara, which, sadly, was sold at auction by her son Viscount Linley. One hopes that it was bought back discreetly by other, more senior members of the Royal Family. If you look up every name and reference (books, photograph and tiara) in this post of mine, you will truly be learning English and English culture.

Bathing implies that you are in the bathtub. In slightly old-fashioned English, it could also suggest bathing in the sea. Either way, your body is fully immersed in the water. If you're washing, you're not fully in the water. By the way, you don't need to say 'myself'. If there's no object, it will be clear from the context that you are washing yourself.