We report results from a search for the lepton flavor violating decays B_{s};{0} --> e;{+} micro;{-} and B;{0} --> e;{+} micro;{-}, and the flavor-changing neutral-current decays B_{s};{0} --> e;{+} e;{-} and B;{0} --> e;{+} e;{-}. The analysis uses data corresponding to 2 fb;{-1} of integrated luminosity of pp[over ] collisions at sqrt[s] = 1.96 TeV collected with the upgraded Collider Detector (CDF II) at the Fermilab Tevatron. The observed number of B0 and B_{s};{0} candidates is consistent with background expectations. The resulting Bayesian upper limits on the branching ratios at 90% credibility level are B(B_{s};{0} --> e;{+} micro;{-}) < 2.0 x 10;{-7}, B(B;{0} --> e;{+} micro;{-}) < 6.4 x 10;{-8}, B(B_{s};{0} --> e;{+} e;{-}) < 2.8 x 10;{-7}, and B(B;{0} --> e;{+} e;{-}) < 8.3 x 10;{-8}. From the limits on B(B_{(s)};{0} --> e;{+} micro;{-}), the following lower bounds on the Pati-Salam leptoquark masses are also derived: M_{LQ}(B_{s};{0} --> e;{+} micro;{-}) > 47.8 TeV/c;{2}, and M_{LQ}(B;{0} --> e;{+} micro;{-}) > 59.3 TeV / c;{2}, at 90% credibility level.