Oops, forgot to mention. Bromeliads bloom only once in their lifetime. The new pup will produce a bloom when it reaches adult size which may take one year or more. Then it produces pups and so the cycle continues.
Some Deuterocohnia have perennial bloom stalks, and will bloom two or three years on the same inflorescence.
They can bloom for seven years on the same stalk
Yes, there are a few exceptions to the one bloom per rosette rule, but most beginners aren't growing these plants.
This thread was a follow-up to this one. Not sure why a new thread was started, but in general, when an old inflorescence turns brown, cut it off. That plant won't bloom again (unless it's a Dyckia or a Deuterocohnia).