I don't know if it's of any help to you now, but I do inner curves first making sure that I have the rest of the applique lying flat as I work. That means that the bias will smooth out on the wider edging and can be slipped under with the needle more easily.
If you stitch the outer (longer) edge down first then either you need to pull the bias wider to tighten it up (and thus alter your applique width or the depth of your turn under) or use micro pleats to contain the volume of the fabric.
Thank you for the tip Saf; I'll have a google for Becky Goldsmith; there's always another way to do something, and it's interesting to see some other ideas.
Mary