We report results of a study of the B oscillation frequency using a large sample of B semileptonic decays corresponding to approximately 1 fb-1 of integrated luminosity collected by the D0 experiment at the Fermilab Tevatron Collider in 2002–2006. The amplitude method gives a lower limit on the B oscillation frequency at 14.8 ps-1 at the 95% C.L. At ms=19 ps-1, the amplitude deviates from the hypothesis =0 (1) by 2.5 (1.6) standard deviations, corresponding to a two-sided C.L. of 1% (10%). A likelihood scan over the oscillation frequency, ms, gives a most probable value of 19 ps-1 and a range of 17<ms<21 ps-1 at the 90% C.L., assuming Gaussian uncertainties. This is the first direct two-sided bound measured by a single experiment. If ms lies above 22 ps-1, then the probability that it would produce a likelihood minimum similar to the one observed in the interval 16–22 ps-1 is (5.0±0.3)%.