It's my guess that you need to take out your bulbs and re-plant them. Most of those bulbs are supposed to be planted six inches or less in the first place. I would think you would smother them with six inches of additional soil. Look at it this way, here's your chance to divide, amend and enrich the soil, and re-arrange what you have for an even better display next year.

One method is to cut out your bed into clumps of 10 or so square inches and lay them aside on a tarp. Add your soil to raise the bed and then return the squares. I've done this before and it preserves all the smaller bulbs that have naturalized in large numbers. Any larger bulbs such as tulips can be stuck back in if they break out of each clump. tulips tend to be shorter lived than the smaller bulbs so it's also not a great loss to replace them with fresh stock.

On the positive side, this is the best time of year to do all this.