Shaving down bridge of nose. Will this make the bottom of my nose look wider or will it be a subtle change?

Shaving down the bridge of your nose will make the bridge straight so your profile view improves.  Depending on how much the bridge is lowered, it can make the bridge look slightly wider but this can be easily corrected.  Photos, at a minimum, would be needed to give you any meaningful input for your specific case.  A face to face consultation, of course, would be ideal to help you understand what could be achieved.  It would also allow some computer morphing of your photos to help illustrate what may be accomplished. 

Photos would be very helpful to determine what you might benefit from. In general, shaving down a bump will not make the lower third of the nose look wider unless you have a significantly wide nose and he narrows the bones as well.