A new technique to measure the ratio of b quark fragmentation
fractions in ppbar collisions is described.  Using a 70 pb-1 sample of
low-mass dimuon trigger data recorded with the Collider Detector at Fermilab,
we identify B mesons by observing the double semileptonic decays b -> c mu X
with c -> s mu X.  By counting the numbers of K*(892)0, K*(892)+ and
phi(1020) mesons produced in association with these muon pairs, we measure the
ratio of strange to non-strange B meson production to be f_s/(f_u + f_d) =
(21.0 +/- 3.6(stat.)+3.8_-3.0(syst.))%.  This measurement is the most precise
available from hadron collisions to date.  Limits on the branching fractions
of semileptonic charm meson decays with K_1(1270), K*_1(1410) and K*_2(1430)
mesons in the final state are also obtained.