I love salsa, I do. Go ahead and judge me. I also love the condiment of the cocktail world, bitters. Recently took a few bottles of bitters and sugar cubes to a New Year's Eve party to help those that weren't huge bubbly fans.
When I got into the beverage industry there were just a handful of bitters to choose from and stock your bar with. Now there's everything from celery to chocolate, and many odd profiles that I probably will never use. Just look at the options on Kegworks alone.
Can you throw bitters on any cocktail? Yes, if you like salsa on your pasta. It has to work in balance and flavor profile, and that's why you should always tip your talented bartender very well. I digress, but a bottle of bitters will go a long way, so don't worry about the cost. They are a good investment that will help expand your home bartender creativity.
What it means: A bitters is traditionally an alcoholic preparation flavored with botanical matter such that the end result is characterized by a bitter or bittersweet flavor. Numerous longstanding brands of bitters were originally developed as patent medicines, but are now sold as digestifs and cocktail flavorings. - (good ol') Wikipedia
More on bitters from Imbibe, and a video from Eater if you are sick of reading for the day.
Make your own: Get out the Mason jars. Here's a recipe from Serious Eats on making your own bitters. There's a lot of recipes available online, so drink and explore.