Most good stories start with a fundamental list of ingredients: the initial situation, conflict, complication, climax, suspense, denouement, and conclusion. Great writers sometimes shake up the recipe and add some spice.
Sorry, folks. We'd love to write a little analysis here for you, but The Bald Soprano just doesn't comply. Ionesco decided to kick off his playwriting career by writing what he called an "anti-play." There's just no basic through-line to analyze here. There's no protagonist who wants anything. There's no conflict that builds to a climax and then is resolved. His characters mostly just chill out, saying things that may or may not mean anything, and then end their evening yelling things at each other that don't make any sense. The Bald Soprano is a great example of a play that breaks all the rules and still manages to kick butt.