How does buyers’ search for bundles generate sorting among heterogeneous sellers? We study competitive search in which buyers assemble bundles through separate transactions, where prices direct search and determine congestion. With two seller types, buyers choose only same-type bundles below a single threshold in cross-type value and cross-type bundles above it. The threshold lies strictly between geometric and arithmetic means of same-type values, so search produces cross-type matching even when types are complements. With a continuum of types, log-supermodularity and submodularity yield unique stable equilibria with positive and negative assortative matching. Positive sorting extends to any fixed number of visits.