Your unknown is probably calcium hydrogen carbonate, Ca(HCO₃)₂.
I think you might have meant to say that when you tested for the presence of CO₃²⁻, the sample bubbled.
That shows that your sample contained CO₃²⁻ or HCO₃⁻, because carbonates and hydrogen carbonates react with acid to produce carbon dioxide gas.
CO₃²⁻ + 2H⁺ → CO₂ + H₂O
HCO₃⁻ + H⁺ → CO₂ + H₂O
Your compound is either a carbonate or a hydrogen carbonate.
Now we turn to the solubility rules.
The important ones are:
- All compounds of Group 1 metals are soluble.
- All NH₄⁺ salts are soluble.
- All hydrogen carbonates (HCO₃⁻) are soluble.
- All sulfates (SO₄²⁻) are soluble except those of Ba²⁺, Sr²⁺, Ca²⁺, Pb²⁺, Hg₂²⁺, and Hg²⁺. The sulfates of Ca²⁺ and Ag⁺ are moderately soluble.
- All carbonates (CO₃²⁻) and phosphates (PO₄³⁻) are insoluble except for those of NH₄⁺ and Group 1 metals (see rules 1 and 2).
Since your unknown is in solution, and all carbonates are insoluble, your unknown must be a hydrogen carbonate.
Since it forms an insoluble phosphate, it must contain Ba²⁺, Sr²⁺, Ca²⁺, Pb²⁺, Hg₂²⁺, or Hg²⁺.
Your unknown is one of Ba(HCO₃)₂, Sr(HCO₃)₂, Ca(HCO₃)₂, Pb(HCO₃)₂, Hg₂(HCO₃)₂, or Hg(HCO₃)₂.
The most likely suspect is Ca(HCO₃)₂ (it's the most commonly available).