I'd say starch it heavily, too, and then handle it gently.
Another suggestion I've read about, but not tried, is to stitch a narrow (1/8") ribbon (like the inexpensive kind they sell in craft stores) along the bias edges. Since the ribbon isn't stretchy, your edges won't be able to stretch out of shape. Just don't iron over the ribbon with your iron on the "cotton" setting -- the ribbon is made of polyester, I think.
I have put bias borders on quilts with no particular problems -- go for it!