Any process that modulates the rate, frequency or extent of branching involved in ureteric bud morphogenesis, the process in which the branching structure of the ureteric bud is generated and organized. The ureteric bud is an epithelial tube that grows out from the metanephric duct. The bud elongates and branches to give rise to the ureter and kidney collecting tubules. [ GOC:yaf GOC:tb GOC:dph ]