  We show how to estimate a broad class of multipartite entanglement measures
from Bell basis measurement data. In addition to lowering the experimental
requirements relative to previously known methods of estimating these measures,
our proposed scheme also enables a simpler analysis of the number of
measurement repetitions required to achieve an $\epsilon$-close approximation
of the measures, which we provide for each. We focus our analysis on the
recently introduced Concentratable Entanglements [Beckey et al. Phys. Rev.
Lett. 127, 140501 (2021)] because many other well-known multipartite
entanglement measures are recovered as special cases of this family of
measures. We extend the definition of the Concentratable Entanglements to mixed
states and show how to construct lower bounds on the mixed state Concentratable
Entanglements that can also be estimated using only Bell basis measurement
data. Finally, we demonstrate the feasibility of our methods by realistically
simulating their implementation on a Rydberg atom quantum computer.
