We present a search for B decays to charmless final states involving charged or neutral a0 mesons. The data sample corresponds to 89 × 106 BB̄ pairs collected with the BABAR detector operating at the PEP-II asymmetric-energy B Factory at Stanford Linear Accelerator Center. We find no significant signals and determine the following 90% C.L. upper limits: B(B0 → a0-π+) < 5.1 × 10-6, B(B0 → a0-K+) < 2.1 × 10-6, B(B- → a0-K̄0) < 3.9 × 10-6, B(B+ → a00π+) < 5.8 × 10-6, B(B+ → a00K+) < 2.5 × 10-6, and B(B0 → a00K0) < 7.8 × 10-6, where in all cases B indicates the product of branching fractions for B → a0X and a0 ηπ, where X indicates K or π.