It will leave Earth's gravitational field with a fair amount of velocity - whether or not you're taking relativity into account. Of course that's assuming the object is small, I'm not sure how much drag one could get at very large sizes.
Anyway, once it's left the gravitational field, it will...
The physics is quite well defined in this area if you simply model the bottle as a cavity with length L - where L (in terms of the bottle) is the distance between the top of the bottle and the surface of the liquid. Fill up the bottle some more and you're reducing L.
In such a cavity, the...