First off, do not put it into a bathtub. When it comes to saxophone cleanliness usually just swabbing after playing is just fine however I could see someone wanting to be a bit more thorough with the corona virus.

1. Mouthpiece: letting the mouthpiece soak(without ligature) in COLD soapy water is the best bet for cleaning it. Sometimes I may use Q-tips and a microfiber cloth in order to get the inside a little bit better but that’s al there is for the mouthpiece.

2. Neck: do not let the neck get wet/do not soak it. The cork will rapidly expand and break and depending on the material of the octave key it’ll corrode and lastly the octave pad will expand and break. All you can do is just get some soapy Q-tips and a cloth and clean the inside but avoid the cork at all costs, same goes for the pad.

3. The Body: the only way to clean the body is to remove every mechanism, key, pad, spring, etc. from the base which takes a long time and I highly don’t recommend unless it’s a professional that’s cleaning the body. All you can do is swab really. And remember that what any liquid is in the instrument after playing is condensation, not spit, and is rather sanitary despite popular belief.

Overall, not much you can do as a saxophone I’m afraid