We present a search for the technicolor particles rho{T} and pi_{T} in the process pp-->rho{T}-->Wpi{T} at a center of mass energy of sqrt[s]=1.96 TeV. The search uses a data sample corresponding to approximately 1.9 fb{-1} of integrated luminosity accumulated by the CDF II detector at the Fermilab Tevatron. The event signature we consider is W-->lnu and pi{T}-->bb, bc or bu depending on the pi{T} charge. We select events with a single high-p{T} electron or muon, large missing transverse energy, and two jets. Jets corresponding to bottom quarks are identified with multiple b-tagging algorithms. The observed number of events and the invariant mass distributions are consistent with the standard model background expectations, and we exclude a region at 95% confidence level in the rho{T}-pi{T} mass plane. As a result, a large fraction of the region m(rho{T})=180-250 GeV/c{2} and m(pi{T})=95-145 GeV/c{2} is excluded.