We study SU(3)-breaking effects in the neutral B_d-bar B_d and B_s-bar B_s systems with unquenched N_f=2+1 lattice QCD. We calculate the relevant matrix elements on the MILC collaboration’s gauge configurations with asqtad-improved staggered sea quarks. For the valence light-quarks (u, d, and s) we use the asqtad action, while for b quarks we use the Fermilab action. We obtain xi=f_B_ssqrtB_B_s/f_B_dsqrtB_B_d=1.268+-0.063. We also present results for the ratio of bag parameters B_B_s/B_B_d and the ratio of CKM matrix elements textbarV_tdtextbar/textbarV_tstextbar. Although we focus on the calculation of xi, the strategy and techniques described here will be employed in future extended studies of the B mixing parameters Delta M_d,s and DeltaGamma_d,s in the Standard Model and beyond.