Branching fractions for decays from the P-3/2 level in B-138 at have been measured with a single laser-cooled ion. Decay probabilities to S-1/2, D-3/2, and D-5/2 are determined to be 0.741716(71), 0.028031(23), and 0.230253(61), respectively, which are an order-of-magnitude improvement over previous results. Our methodology only involves optical pumping and state detection, and is hence relatively free of systematic effects. Measurements are carried out in two different ways to check for consistency. Our analysis also includes a measurement of the D-5/2 lifetime, for which we obtain 30.14(40) s.