Dissolving sand (or something similar) in a bottle of water?
To clarify: it sounds like you want a layer of insoluble sediment, so that if you shake the bottle, the water looks cloudy. Maybe it settles back out quickly, or maybe the water stays cloudy.

Then, you add something and shake the bottle again. This time, the sediment disappears.

There are lots of possibilities here. One that comes immediately to mind is lime (calcium hydroxide), which is only slightly soluble in water. Add acid (vinegar if you're timid and don't mind adding a large quantity, hydrochloric acid if you want fast results), and it will be converted to a highly soluble salt.

Chalk (calcium carbonate) would work, too, but it would fizz (produce bubbles of gaseous carbon dioxide) when you added the acid.

If you can say a little more about the context of your demonstration, we might be able to provide better ideas. Is this actually about solubility, or is it a metaphor for something else?