I would cut off the main flower stalk and leave the leaves for a while to photosynthasise. This is when a plant takes the light from the sun to energise for next years growth. I would leave them on for a couple of months then you can cut them off and let the bulb dry out.

I usually dead head the plant and take the full stalk off. As Andrea says leave the plant to grow. give it a feed too to help it build up a flower for next year. Sometimes they dont flower until the year after but they will then.
welcome to GoY too.

An expert grower told me to just take the flower head off....leave the scape (stem) to die back, the goodness will die back into the bulb....keep on watering(and feeding) until the leaves start to die....then withhold water until the bulb shows sign if re-growth...If anyone wants full instructions (from holder of national collection) pm me and I will send...