Just a guess because Wikipedia says that angostura bitters are made from a secret recipe. The insoluble spices and such inside provide a sites of nucleation for CO2 bubble formation which causes the fizzing. You can see this effect when putting salt into boiling water, like before throwing in some pasta to cook. Salt is soluble but the first moment after dropping in the salt you will notice fizzing and bubbling being concentrated in the area where the salt went, this effect quickly terminates due to the salt dissolving in the water.
Again, just a guess.