  We report the experimental generation of all four frequency-bin Bell states
in a single versatile setup via successive pumping of spontaneous parametric
downconversion with single and dual spectral lines. Our scheme utilizes
intensity modulation to control the pump configuration and offers turn-key
generation of any desired Bell state using only off-the-shelf telecommunication
equipment. We employ Bayesian inference to reconstruct the density matrices of
the generated Bell states, finding fidelities $\geq$ 97% for all cases.
Additionally, we demonstrate the sensitivity of the frequency-bin Bell states
to common-mode and differential-mode temporal delays traversed by the photons
comprising the state$\unicode{x2013}$presenting the potential for either
enhanced resolution or nonlocal sensing enabled by our complete Bell basis
synthesizer.
