I went through this as well. My Ibby is very sympathetic-resonance-happy.

I tried about everything, including many other basses at a local music store. The better they were tuned, the more the resonance took place. I also used foam mutes near the bridge. I gave other bridges a serious consideration. In the end it all came down to me not muting smart and accurately. I stopped learning how to play and started learning how to mute instead. Every night, seven days a week I practised muting using several styles until it became a natural habit. You also may ask yourself which string to use; open D, or maybe better fifth fret on A? Now I use floating thumb and 'unused' fingers of the fretting hand while fingering. If I'm picking it mainly comes down to the fretting hand and the palm of the picking one. Ringing strings is no issue anymore.