I recently had a very similar experience, and have insisted on a referral to a cadiologist. It has been a bit of a wake-up call for me, since I exercise regularly, don't smoke, maintain an ideal weight and generally exhibit none of the factors which some suggest accompany Left Bundle Branch Block (LBBB) and which are thought by some to be causal (e.g., high blood pressure, coronary artery disease, etc.).

Basically, LBBB is an abnormality of electrical conduction in the heart that sometimes expresses itself in arthymias.  Sometimes it seems to occur in otherwise healthy individuals, but it is usually a sign of underlying heart disease, which may be serious, and the possibility of this should be thoroughly investigated. Even if not accompanied by other detectible heart problems, seems to increase the risk of out-of-hospital cardiac arrest and sudden death. There is apparently not much by way of treatment of the LBBB itself (other than pacemakers, which are sometimes recommended). At the very least, a little more research on the web will encourage you to seek further medical advice.

Hope this is helpful.