In reality, the task of treating Bai Zhanji could have been completed just with Ye Weiming's current medical skills, even without Ping Yizhi's help.
However, Huang Shouzun previously stated that he would "teach him some swordsmanship based on the task completion". This demanded Ye Weiming's cautious approach. If he took shortcuts and didn't find the best doctor, the likely outcome would be missing out on learning a couple of sword moves.
That would have resulted in a loss greater than the gains.
After handing over the task, it was time to run errands.
Players inevitably have to run around for their tasks. For example, after Ping Yizhi agreed to treat the patient, Ye Weiming returned to the Constable's Office to report to Huang Shouzun that everything was ready. Huang Shouzun then asked him to bring Bai Zhanji from Luoyang to the Constable's Office and find Ping Yizhi so that he could treat him there.