A search for the rare, flavour-changing neutral current decay B(sup +) (yields) K(sup +) (nu)(bar (nu)) is presented using 81.9 fb(sup -1) of data collected at the (Upsilon)(4S) resonance by the BABAR experiment. Signal candidate events are selected through the identification of a high momentum charged kaon and significant missing energy, where the companion B(sup -) in the event has decayed semileptonically via B(sup -) (yields) D(sup 0)(ell)(sup -)(bar (nu)) X and X is kinematically constrained to be either nothing or a low momentum transition photon or (pi)(sup 0). The analysis was performed blind and 6 candidates were selected with a background expectation of 3.4 (+-) 1.2. This leads to a limit on the branching fraction of (Beta) (B(sup +) (yields) K(sup +) (nu)(bar (nu))) < 7.2 x 10(sup -5) at 90% confidence level. We also search for the reaction B(sup +) (yields) (pi)(sup +)(nu)(bar (nu)) and extract a limit on the branching fraction of (Beta)(B(sup +) (yields) (pi)(sup +)(nu)(bar (nu))) < 2.5 x 10(sup -4) at 90% confidence level.