  We present a search for the rare decays B+ -> K+ nu nubar and B0 -> K0 nu
nubar using 459 million BBbar pairs collected with the BaBar detector at the
SLAC National Accelerator Laboratory. Flavor-changing neutral-current decays
such as these are forbidden at tree level but can occur through one-loop
diagrams in the Standard Model (SM), with possible contributions from new
physics at the same order. The presence of two neutrinos in the final state
makes identification of signal events challenging, so reconstruction in the
semileptonic decay channels B -> D(*) l nu of the B meson recoiling from the
signal B is used to suppress backgrounds. We set an upper limit at the 90%
confidence level of 1.3 x 10^{-5} on the total branching fraction for B+ -> K+
nu nubar, and 5.6 x 10^{-5} for B0 -> K0 nu nubar. We additionally report
partial branching fractions in two ranges of di-neutrino mass squared for B+ ->
K+ nu nubar.
