What is the connection between right bundle branch block with slow heart beat?

It depends. Right bundle branch block (rbbb) in itself is usually a benign disturbance of conduction system of the heart. It usually does associated with adverse effects. However, it may be a part of other serious conduction disorders of heart (like high degree av block). Therefore, it may not be the cause of but a part of findings in a slow heart rate. Also remember, slow heart rate is not always bad.
None. Slow heart rate is controlled by the sinus node (in the right atrium) and has nothing to do with the bundle branches which are in the interventricular septum. Drugs and diseases that affect the sn have little or no effect on the rbb.