Bitters are used (almost entirely) to round out the flavour of cocktails, adding subtle — but much needed — bitter, herbal notes. Unless you’re a fan of bitters and sparkling water, you rarely get a taste of the bitters themselves; they just make other things taste better.
This is true of cocktails, and it’s also, oddly, true of picnic salads, particularly potato salad, macaroni salad and (perhaps more obviously) fruit salad. For the mayo-based situations, the bitters add their characteristic botanical flavour, creating dimension and cutting through one-note richness without tasting like outright gentian root.
The Angostura bottle suggests a few dashes per cup of mayonnaise or dressing, but I doubled that, as mayo tends to mute other flavours. Start with a couple of dashes of bitters per cup of salad, not mayo, then increase to suit your taste.
For fruit salads — or even green salads — you won’t need as much, as you won’t have mayo to contend with. Start with a cup of vinaigrette, and add couple of dashes to the dressing, give it a taste, and add more if you want.
Your salads will taste instantly more sophisticated, and no one will be able to guess your secret ingredient. (If they do, know that you have a professional drinker on your hands, and make a note to keep them hydrated.)