Reminds me of when, as a kid, I spent hours making a model motorbike by cutting up chunks of polystyrene, then painted it with the Humbrol enamels that I had to hand.
It looked amazing when freshly painted.
Only to dissolve to a brightly-coloured resiny lump within a few hours. I was devastated!
So the humbrol enamel will dissolve the plastic bottle, my main plan is to sand the area a little roughly and then paint it.