We report the analysis of the three-body e(+)e(-) -> B (B) over bar pi(+/-), B (B) over barpi(+/-), and B(B) over bar* pi(+/-) processes, including the first observations of the Z(b)(+/-)(10610) -> B (B) over bar* + c.c. and Z(b)(+/-)(10650) -> B*(B) over bar* transitions that are found to dominate the corresponding final states. We measure Born cross sections for the three-body production of sigma(e(+)e(-) -> B (B) over bar* + c.c.pi(-/+)) = [17.4 +/- 1.6(stat) +/- 1.9(syst)]pb and sigma(e(+)e(-) -> B*(B) over bar*pi(-/+)) = [8.75 +/- 1.15(stat) +/- 1.04(syst)] pb and set a 90% C.L. upper limit of sigma(e(+)e(-) -> B (B) over barpi(-/+)) < 2.9 pb. The results are based on a 121.4 fb(-1) data sample collected with the Belle detector at a center-of-mass energy near the Upsilon(10860) peak.