Through an amp? You've recorded stuff, made the change, and re-recorded?
I'm not attacking, or even doubting. I'm honestly asking. If you have, you are more perceptive than me.
I ask because I did this a couple years ago on another forum with a bunch of stuff, mostly pickups (guitar, not bass) and we were all amazed at how little - like, infinitesimal - difference stuff makes once you run through an amp and cabinet. Supposedly hearing is the sense with the poorest 'memory', don't know if that's true or not, but my experience supports it.
Comparison recordings? Oh god no...I know in most cases it wouldn't show anything. What I'm talking about is probably not overt enough to be obvious in a recording but lot of it depends on the particular bridge. The difference between a heavy brass bridge and a Danelectro type wood saddle is extreme and I'm sure most people could hear that recorded. Between a Badass and a vintage threaded rod you probably couldn't. But that's not to say it's won't make a big picture difference in the sound of the music you play. Something I notice to pretty minute degrees is the feel of the vibration of the strings between different bridges....I prefer lighter bridges a lot because I like the way they feel more than any super obvious sonic changes. A friend of mine is involved in prototyping titanium vintage Fender replacement bridges. From what I've seen so far I'll probably try one because of the super alive feel it has. A bridge is just one component in a system that includes the idiosyncratic perceptions of the player.
In a lot of ways you're very right though and anyone changing a bridge expecting to have their world rocked will be badly disappointed....it's not something you're going to get a huge amount of bang for your buck change out of like you would swapping pickups or strings. But where one might say "infinitesimal" another might say "subtle" and subtle counts. We're kinda into that grey area where if it makes a difference to me it makes a real difference and it doesn't really matter if my perception is more keen than yours or just my imagination....you can't measure it so who's to say?
I guess I just don't want to see anyone dissuaded from experimenting and finding out for themselves. If I hadn't tried different bridges I wouldn't have discovered how important the feel differences are to me. Ultimately these are tools for creating art......logic and empirical measurements aren't always the whole story of the end result.