Can someone tell me the net ionic equation of solid barium sulfite and hydrochloric acid? Confused whether to break down the compound BaSo3 into its ionic form.

This is what I have:

Molecular equation:
BaSO3(s) + 2HCl(aq) --> BaCl2(aq) + H20(l) + SO2(g)

Ionic (this is where I'm confused. Does the solid compound dissociate with HCl?):
Ba2+(aq) + SO3 2-(aq) + 2H+(aq) + 2Cl-(aq) -->Ba2+(aq) + 2Cl-(aq) + H2O(l) + SO2(g)

I'm not sure either, but we usually do not cross out the solids in an ionic equation, so that we get:

BaSO_3 (s) + 2H^+ (aq)\rightarrow Ba^{2+} (aq) + H_2O (l) + SO_2 (g)