Looks like the iris you have is the re-bloomer called Immortality, especially if it has a small bit of yellow on the beard. (photo below) It's pretty hardy. Iris have whats called a rhizome, not a bulb
, it's more like a stem then a root, and therefore it should be left partly exposed. I've heard it said that you should think of the rhizome as a duck on water. The feet and part of the body under water, and the rest above it. For best results, dig a hole and put a handful of bone meal down there and then cover it with soil. Then make a mound of soil and put half the roots on each side of it, and then pack the dirt in over the roots, but leave the rhizome about half way exposed. It's really important NOT to use mulch around them. It holds too much moisture and can cause rot, which will kill the iris. It's best to clip the leaves off to about 5 or 6 inches, otherwise the wind can uproot them until the roots get established. Good luck, and visit the iris forum, you'll find some great people and see some nice irises.