We give a geometrical construction of Connes spectral triples or noncommutative Dirac operators \def\Dslash{{\mathrlap{\,/}{D}}}\Dslash starting with a bimodule connection on the proposed spinor bundle. The theory is applied to the example of M_2(\mathbb C) , and also applies to the standard q -sphere and the q -disk with the right classical limit and all properties holding except for \mathcal J now being a twisted isometry. We also describe a noncommutative Chern construction from holomorphic bundles which in the q -sphere case provides the relevant bimodule connection.