Lots of bromeliads get little blue flowers growing off the side or top of an inflorescence, which itself might be a crown or a blade or a slight mound. I've never been able to get a T cyanea to rebloom. They're easy to grow, but fussy to bloom.
Unlike many broms and especially other Tillandsias, a T cyanea prefer its feet to be in soil and wants to be watered conventionally. They should be sprayed/misted frequently, like others, but you should water the soil like a conventional plant too.
Keep an eye out for bromeliads on quick-sale racks, since the parent plant dies after blooming and they're often sold for a fraction of the original price afterwards. But that's when they grow their pups and some will grow many of them. Some will last a long time after blooming, but the clock is running and it'll never bloom again.