I have experimented with the Boulder Bidet for backpacking. It works 85%. I still bring paper, but much less. Hygiene is much improved. The paper is used to check that you are clean.
The setup weighs less than a full roll of paper, and there is less to either bury or pack out.
The trick is practicing, this is not something to rely on or expect to work without practice. Biggest advice, squeeze the bottle as hard as possible and learn how to aim it.
I bought 2, and one lives in the bottom drawer at work. This keeps me clean and in practice.
Putting this back in your pack sound dirty? You are supposed to wash it with soap and water, same as you are supposed to do with your hands.
The Boulder Bidet website is useful to teach you about it, and the concept. Available there and Amazon, about $15.
There is something similar that slips into the neck of a disposable water bottle, called Hygienna Solo. I ordered one of those as well, and I can say that it is utterly awful.