The stick inks are carbon based, like india ink. They do not dissolve.
Waterproof ink can have several definitions, sometimes meaning the ink contains shellac. The stick ink does not qualify as waterproof under this definition, but I'm guessing your bottled ink will not either. The stick ink shares the same qualities as other carbon-based inks.
Part of the charm is the meditative process of grinding. The stick ink, the inkstone, the brush, and the paper are the four treasures of the traditional Chinese scholar.