zinc oxide is an ionic compound, you better not think of it in terms of covalent bonds (like a thiol)
zinc is charged 2+, oxygen 2-, that is what "binds them" in a lattice.
and to dissolve zinc oxide you will need a lot of acid, or indeed alkaline. But realize that the zinc oxide will then react with the acid/base, so it will not be the pure compound that dissolves. You will either have zinc cations with the acid's conjugate base ion, or you will have a complex.