We have searched for the decays B^0_s -> e^+/- mu^-/+ and B^0_d ->
e^+/- mu^-/+ using a 102 pb^-1 data sample of ppbar collisions at sqrt s = 1.8
TeV collected with the Collider Detector at Fermilab.  We set upper limits on
the branching fractions of B(B^0_s -> e^+/- mu^-/+) < 6.1(8.2) x 10^-6 and
B(B^0_d -> e^+/- mu^-/+) < 3.5(4.5) x 10^-6 at 90(95)% confidence level.
Using these limits, we set lower bounds on the corresponding Pati-Salam
leptoquark masses and find that M_LQ(B^0_s) > 20.7(19.3) TeV/c^2 and
M_LQ(B^0_d) > 21.7(20.4) TeV/C^2 at 90(95)% confidence level.