This species and many alpinia will bloom after at least a full year of growth (on mature clumps). A. zerumbet tends to bloom in late spring, so old growth refers to a stem that is usually about 16months or so old and is at full size during the normal bloom period. One stem blooms only once so you can cut it down if you want. They won't get much taller than what you have now. If you cut a stem at any level before it blooms, it won't bloom. The only pruning you can do with gingers is cutting off old dead or dying (already bloomed) stems, anything else is just preventing the blooming from every happening.

Tim Chapman

Listen to Tim. He got it exactly right. Thats why if you live in an area with freezes you will never see the Alpinias bloom. They will come back from the roots if well protected but never bloom which isn't such a big deal since the leaves are so awesome on their own. The flowers are cool too of course. I've a place in New Orleans and we get blooms most years due to our warmer winters.
Mike