Entangled photon pair sources based on bulk optics are approaching optimal design and implementation, with high state fidelities, spectral purities and heralding efficiencies, but generally low brightness. Integrated entanglement sources, while providing higher brightness and low-power operation, often sacrifice performance in output state quality and coupling efficiency. Here we present a polarization-entangled pair source based on a hybrid approach of waveguiding and bulk optics, addressing every metric simultaneously. We show 96 % fidelity to the singlet state, 82 % Hong-Ou-Mandel interference visibility, 43 % average Klyshko efficiency, and a high brightness of 2.9 × 106 pairs/(mode·s·mW), while requiring only microwatts of pump power.