| Any effect the bridge is going to have on the tone of the bass is pretty subtle. And, change doesn't always account for better. Sometimes, it's just change.
Swapping to a more rigid, higher mass bridge MAY improve the sustain a bit and/or offer a bit more focused fundamental. It's more likely if the existing bridge is especially flimsy or otherwise poorly designed. If the bridge on the bass is fairly sturdy and well-coupled to the body, a difference is less likely.
In your case, considering what you want, you may discover that a bridge swap does absolutely nothing to get you where you want to be. Or, even worse, it could actually make the bass less mid-centered. | 
