I did a thread quite some time ago on threaded inserts & also in the same thread got into doing some testing with high mass bridges vs standard Fender-style bent bridges & did some A/B audio comparisons as well as A/B frequency analysis of the waveforms ran through a spectrum analyzer.
My conclusion from the testing I did is that the mass & material of a bridge does have slight tonal effects, but don't expect the sky to open & the seas to part. It will still sound like your bass with very subtle tone differences if you are able to audibly perceive it. At best (depending on your ear) you may hear slight differences in overall punch & maybe some extra top end (depending on bridge material, brass, aluminum, etc), but again
subtle is the operative word. I've seen some YouTube videos of A/B audio on bridge changes & on a couple, I could hear very slight differences. They say bridge material will sound different from each other (brass, aluminum, steel) & I'm sure they do - each in their own subtle way.
But in all honesty, I would recommend a bridge upgrade based on performance & functionality upgrade purposes rather than looking for huge tonal changes or even fairly noticeable changes. Because IME, the tonal changes brought by most bridge changes are so slight that they'd surely be lost in a mix anyway or negated by the tiniest of EQ twiddling. To be honest, I've heard way greater tonal changes come in the form of trying new brands of strings rather than any bridge change I've done in the past. Personally, I'd only change bridges for design/functionality preferences like quick-release string changes, elimination of side-to-side saddle movement, adjustable string spacing in some cases, etc. YMMV.
