I doubt this has any connection to the manner in which bishops wear rings. While bishops do indeed wear their rings on the right ring finger, wearing a ring on the right hand is not generally regarded a mimicking a bishop. Rather, many people (both women and men) wear all manner of rings on their right ring finger that are used just as ordinary jewelry. For example, my uncle wears a ring on his right ring finger that is something of a family heirloom. It has no special significance other than this.
Something else we should keep in mind, the whole idea of wedding rings for men is an innovation from the 20th Century. Before that, only women wore wedding rings. Men still wore rings, of course, just not wedding rings.
Further, it is not a universal tradition to wear a wedding ring on the left hand. While it certainly is the custom in the English-speaking world, in many Eastern-European counties, wedding rings are worn on the right hand.