That’s for at home. But to answer your other question, I do carry a small 50ml squeeze bottle of liquid soap in my bag, like those keychain hand sanitizers. Obviously it’s not always useful if the public toilet doesn’t have a bidet in the first place, so I also have wet wipes in my bag for a cleaner feeling at least until I can get home and wash properly.

And to answer your one other question, yes portable bidets exist. I have one and bring it with me when I travel so I can still wash if my hotel doesn't have one.