The bell is used as a reminder that there is a High Priest (Jesus Christ) who continually makes intercession for us. The high priests in the Old Testament wore bells on the hem of their garments while making intercession for the people. As long as the bells were heard the people knew that the high priest was alive and their petitions and requests were granted for another year.
So too, by ringing the bell we daily remind ourselves that Jesus our High Priest is continually in the presence of God making intercession for us. All his promises are yea and amen. We have this confidence that if he hears us then he answers our petitions and requests.