  We present our results of lattice calculations of $B$ parameters, which
parameterize $\Delta B$=2 transition amplitudes together with the leptonic
decay constant. Calculations are made in the quenched approximation at
$\beta$=5.7, 5.9, 6.0 and 6.1, using NRQCD action for heavy quark and the
$O(a)$-improved Wilson action for light quark. The operators are perturbatively
renormalized including the correction of $O(\alpha_s/(aM)^m)$ ($m\ge$0). We
examine the scaling behavior of $B$ parameters, and discuss the systematic
uncertainties based on the results with several different truncations of higher
order terms in 1/M and $\alpha_s$ expansions. We find
$B_{B_d}(m_b)=0.84(3)(5)$,
$B_{B_s}/B_{B_d}=1.020(21)(^{+15}_{-16})(^{+5}_{-0})$ and
$B_{S_s}(m_b)=0.85(1)(5)(^{+1}_{-0})$ in the quenched approximation. The errors
represent statistical and systematic as well as the uncertainty in the
determination of strange quark mass.
