Well, whoever wrote that pronunciation suffered from "seseo", which is pronouncing c and z as a s. It is NOT the correct pronunciation, although is absolutely commonplace in South American and South Spanish dialects.
Z has a proper sound that is quite different from s so it should be "bahn-zo". But with an even softer z sound that the usual in English, which is closer to s than to Spanish z. It's hard to explain, but certainly those saying "Bone-so" are suffering from seseo. Specially if the guy is supposed to be from Madrid. We are unable to pronounce d's at the end of a word (such as in: Madrid), but we certainly can pronounce a z properly. Did Not Do The Research.
Question for you. There's a character in a book I read who's from Madrid and his name is Bonzo. The book gives the pronunciation of his name as "Bone-So", not "Bahn-zo." And now there's a small argument in the fandom for this book because most people pronounce the name as "Bahn-zo" and not "Bone-so" and I'm just like let me ask Went because he will lead me to a better answer.