I would add - practice thinking it before doing it. Try thinking of riding with one hand, steering with one hand, and just relaxing the other, or removing it briefly from the bars without doing anything with it. Just feel what it feels like, you may feel that you have to use your core more to stay in balance.

Once you have a feeling for how you actually ride your bike with only one hand without veering or wobbling you can start thinking about what you want to do with that spare hand

Try isolating the leaning forward movement too, try practicing it while riding without actually touching the bottle or removing your hands. It helps if your body recognizes part of the movement pattern from before.