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Entanglement is not only the resource that fuels many quantum technologies but also plays a keyrole for some of the most profound open questions of fundamental physics. Experiments controllingquantum systems at the single quantum level may shed light on these puzzles. However, measuring,or even bounding, entanglement experimentally has proven to be an outstanding challenge, especiallywhen the prepared quantum states are mixed. We use entropic uncertainty relations for bipartitesystems to derive measurable lower bounds on distillable entanglement. We showcase these boundsby applying them to physical models realizable in cold-atom experiments. The derived entanglementbounds rely on measurements in only two different bases and are generically applicable to anyquantum simulation platform.