I've made a bubble hem skirt from a pattern and how it worked was to have a straight lining layer and a flared outer layer. Once you've sewn the side seams together, sew the bottom of the two layers together to form the bubble hem, and then attach the waistband as usual to form the skirt.

In the bubble skirts I have made, you simply stitch two long machine stitches around the bottom hem (one a quarter of an inch above the other), then pull the ends to gather the material. This gathering creates the "bubble". You should probably also add a lining piece that attaches to the gathered hem and the waistband, to hold the hem up and shrink your skirt length (or use the existing lining), just like Passion Flower suggested.