Are bisulfates and bicarbonates soluble in water?
According to it's Wikipedia page, calcium bicarbonate is not a known solid compound, but it does exist in solution, presumably prepared by dissolving calcium carbonate and bubbling carbon dioxide through the solution until bicarbonate dominates the following pH-dependent disproportionation:

$$\ce{2HCO3- &lt;=&gt; H2O + CO2 + CO3^2-}$$

It apparently has a solubility of 16.6 g per 100 mL of water at room temperature. which is about a 1 M solution. 

Magnesium bicarbonate similarly exists only in aqueous solution, though it is much less soluble at 0.077 g / 100 mL.

As solids, these salts probably fall victim to the following equilibrium( $\ce{M}$ is a generic divalent metal:

$$\ce{M(HCO3)2 &lt;=&gt; H2O + MCO3 + CO2(g)}$$

The carbon dioxide escapes, preventing the system from ever staying at equilibrium.