Beneath Alice's dress is a striped petticoat with a bias edge shown here in a photo taken of the actual original costume on display.

Not knowing what the actual petticoat looked like under the dress (as you can only see the hem in the photos), we imagined that the construction of the petticoat was similar to the dress i.e. half way down a straight skirt and then the other half a gigantic ruffle.  The straight and the ruffle were cut and serged and then we gave the ruffle a rolled edge on the top as an accent.  Then the ruffle was gathered and attached to the straight skirt.

A long piece of fabric cut on the bias was made into a thick bias tape to edge the bottom of the petticoat and give the direction change in the stripes.  Here we are pinning the bias tape to the hem to get ready for stitching.

Once it was stitched into place it was pressed and then folded over again to conceal all the seams.