Its is possible for a molecule to have a polar bond but have an overall polarity of nonpolar?

A molecule can possess polar bonds and still be nonpolar. If the polar bonds are evenly (or symmetrically) distributed, the bond dipoles cancel and do not create a molecular dipole. For example, the three bonds in a molecule of BF3 are significantly polar, but they are symmetrically arranged around the central boron atom. No side of the molecule has more negative or positive charge than another side.