We report on a sample of Jψ mesons coming from secondary vertices, a characteristic of heavyquark decay, detected in the Fermilab Meson West spectrometer. Based on eight signal events in which a Jψ emerges from a secondary vertex occurring in an air-gap region, we obtain an inclusive bb¯ cross section of 75 ± 31 ± 26 nb/nucleon. This result is compared to recent QCD predictions. We have also observed several events in the exclusive decay modes B±→Jψ+K± and B0→Jψ+K0* in which the B mass is fully reconstructed.