RBBB showed up on my Class One renewal just after I started my first flying job (in fact I received the letter from the CAA the night before I started line training). My medical wasn't pulled straight away and I continued with my training while I arranged the various tests.
It seems that they are most worried about RBBB being a symptom of something worse. In my case I had to have a stress ECG, 24 hour ECG and an echo-cardiogram. All of which showed that the rest of me was functioning normally. The whole process took a couple of months and I remained flying throughout. The only thing they did was to restrict my medical to "as or with a co-pilot" while I underwent the tests.
If I can help in any way - just ask.