Most (if not all) bromeliads die after reproducing. Grow the pups. I'm sure if you google tillandsia care, you'll find plenty of info.

I do not separate the pups from this plant until I have quite a few of them. The pups may not bloom next year, but they should bloom the following year. For me it is fairly slow growing.

See post below (or it may be above after I add this info) called "Is it too late to save my Tillandsia Cyanea "Pink Quill" plant?" because that's what your plant is. Also, I think you're doing okay with it, so keep doing that, just don't be surprised if the main, original plant slowly dies away, making room for the pups/offsets/daughter plants. They can all stay where they are until they seem to be pushing out of the pot then you can repot if you wish, or if you want to separate them, wait until the babies are at least half the size of the mother plant. In the wild the plant would remain as one until something comes along to trample it, play with it, and/or eat part of it, thus separating it and allowing the babies (or teenagers if large enough) to grow on their own.