You can dig them up but do not store them straight away. Re-plant them in a corner of your garden as the bulbs need to be fed, fattened and strengthened, through the leaves, that you must not cut off until they die. Then you can dig the bulbs again, clean and store in saw dust until September or October when you plant them again for next year.

One thing you have to do immedeately after the flowers have faded is to cut off the flower stems or the fleshy part at their tips, otherwise the plant will spend a lot of energy producing fruits, process that will weaken the bulb.