Yeah, I would guess the coating on that purse is more of a plastic, in which case weathering it would involve rubbing it with something abrasive. But I don't know that that would work. To deepen the color, you could water down like a rosy-colored acrylic, or use gouache, as a thin coating on top of the purse. You would probably have to allow it to be expressive with streaks, because it would be hard to get an even coat without air brush.
A great thing that would also not wash off with water would be an egg tempera wash. You could get a chalk pastel in the color you want, or even use an old eyeshadow tin, and mix it well with egg white and maybe a tiny bit of water. Then brush that on. More likely to stay.
And very last, you can just use a bronze metallic spray paint. If you were using metallic paint, I would choose that over acrylic.
This all sounds madly experimental, but like it could be fun, if you are not too attached to the results.