There are a huge number of bromeliads and many require very different conditions. Do you know what it is, or at least the genus name? A photo would help. Sometimes the pups need to be left a bit longer on the parent plant before removing. A good soaking before repotting often helps. Some people spray with a weak sugar solution, I use weak molasses solution.

Picture of plant's pups.....

Picture of plant's flower....

The mother plant (with the flower) will eventually wilt back to the soil line. You could cut back the leaves or remove the entire mother part anytime that it looks unpleasent along the way to die back.

If left alone the pups would eventually push the original parent out of the pot.

Pups remaining should flower again in a couple years given you plenty of time to repot them seperatly if wanted.

That's a Guzmania, they prefer more shade and moisture than most other bromeliads. That flower is only just opening so it's likely to last a long time yet. Pups are better left until the parent plant is starting to decline, as suggested above. The Guzmanias also tend to like more fertiliser than many other bromeliads, but be mindful that it still should only be about orchid strength and not more.