The plays of Ionesco, along with the work of Samuel Beckett, Jean Genet, and Arthur Adamov, became the foundation for the theatrical movement known as the Theatre of the Absurd. This movement was defined by Martin Esslin in his famous book entitled (you guessed it) The Theatre of the Absurd. On the whole, these writers seemed to be inspired by the philosophy of Existentialism popularized by Jean-Paul Sartre and the idea of the Absurd as articulated by Albert Camus. Basically, they believe that there is no greater purpose in life, therefore everything we do is meaningless or absurd. Ionesco said that, "Absurd is that which is devoid of purpose. Cut off from his religious, metaphysical, and transcendental roots, man is lost; all his actions become senseless, absurd, useless" (source). In the minds of the Absurdists, it was each individual's responsibility to create meaning for themselves. This philosophy can be seen throughout The Bald Soprano.
Fire Chief: [moving towards the door, then stopping] "Speaking of that--the bald soprano?" [General silence, embarrassment]
Mrs. Smith: "She always wears her hair in the same style."
Fire Chief: "Ah! Then goodbye, ladies and gentlemen." (472-474)
What in the world is going on here? Why is everybody embarrassed that the Fire Chief mentions the Bald Soprano? And why does Mrs. Smith's line seem to satisfy the Fire Chief in some way? There's really no telling. In his essay, "The Bald Soprano: A Tragedy of Language," Ionesco says, "one of the reasons why The Bald Soprano received this title is that no prima donna [soprano], with or without hair, appears in the play. This detail should suffice" (source). Thanks Ionesco, that's not very helpful. Sometimes we think he's deliberately messing with our heads.
Basically, we advise you to not stress out too much trying to figure out the title of The Bald Soprano is supposed to mean. The play is purposefully full of all kinds of nonsensical things. The pertinent question is probably not, "Why is the play called The Bald Soprano?" but instead, "Why shouldn't it be?"