Answer: Tulips must grow and fully mature their foliage before it is removed, otherwise they are not able to rebuild their strength to bloom again. So, ideally you would wait until some time in June. But it doesn't sound like that is possible.
If you want to save these, you could try to transplant them either now or enjoy the display and transplant right after they bloom. (Transplanting is more difficult when there are flowers.) Carefully take a ball of soil around and under each bulb (with its roots) and replant immediately at the same depth as it grew before; water after planting to settle the soil and remove any air pockets.
Otherwise, wait as long as possible and then transplant immediately as above. I should mention that it is probably not worth the effort of transplanting unless you have a type of tulip that perennializes well. Many tulips really only do well for the first year or two in the garden and then need to be replaced anyway.
Good luck with your tulips!
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