Last year, I moved some wild purple irises from a shady area to a sunny area. At that time, they bloomed in late May. This year, they had no buds on them at all by May 18. Is there a chance they will bloom this year, or ever? Any recommendations?

It sounds like you moved some blue flag (Iris versicolor). Blue flag will tolerate full sun to light shade, but prefers wet meadows, stream banks and marshes. This has not been a warm spring, as in past years. Their time to bloom is late spring to mid-summer, so give them time. However, make sure there is sufficient moisture in their new location and that you have not transplanted the rhizomes too deep. As with all irises, placing the root systems horizontally just below the soil surface is best. It may take another year before they acclimate to the move and their new site before they establish and bloom.