Observation of B(+)-> b(1)(+)K(0) and search for B-meson decays to b(1)(0)K(0) and b(1)pi(0)

We present the results of searches for decays of B mesons to final states with a b(1) meson and a neutral pion or kaon. The data, collected with the BABAR detector at the Stanford Linear Accelerator Center, represent 465 x 10(6) B (B) over bar pairs produced in e(+)e(-) annihilation. The results for the branching fractions are, in units of 10(-6), B(B(+) -> b(1)(+)K(0)) = 9.6 +/- 1.7 +/- 0.9, B(B(0) -> b(1)(0)K(0)) = 5.1 +/- 1.8 +/- 0.5 (< 7.8), B(B(+) -> b(1)(+)pi(0)) = 1.8 +/- 0.9 +/- 0.2 (< 3.3), and B(B(0) -> b(1)(0)pi(0)) = 0.4 +/- 0.8 +/- 0.2 (< 1.9), with the assumption that B(b(1)->omega pi) = 1. We also measure the charge asymmetry A(ch)(B(+) -> b(1)(+)K(0)) = -0.03 +/- 0.15 +/- 0.02. The first error quoted is statistical, the second systematic, and the upper limits in parentheses indicate the 90% confidence level.