Question

Only covalent bonds can be polar and non-polar, right?

Answer 1

Why would a polar covalently bonded molecule in which the molecule possess an electrical charge?? What's non-polar and polar again? One doesn't like water right?

Answer 2

covalent bond is simply a term that dictates the sharing of electrons between two atoms, it does not imply that the atom in which that bond is made has to be neutral or charged.

Polarity depends on the whether if a net dipole exist within the molecule that is considered, and you are correct in saying that non-polar compounds are water fearing (doesn't like water). An example of a non polar compound would be CH4 methane, all bonds are covalent but there is no net dipole. For a polar compound such as HCN (hydrogen cyanide) a net dipole exist on the molecule making it polar.

A polar covalently bonded molecule that contains a net charge would be NH4+ ammonium ions, if the molecule contains a net physical charge, it is not considered to be neutral but rather in an ionic form.