The starch keeps the folds sharp, and the sharp folds keep it even. Have you ever used the Clover bias tape makers? They are easy once you get the hang of them. (I used it upside down the first few times. When all else fails, read the directions.....). You might want to pick up one of the Clover bias tape makers and try it out. It's a lot less work than other methods I have tried, and works great for me. The tape makers come in different sizes. You want the type with a colored plastic insert (color-coding of size) as this works the best. Here is a link to the one I like:
http://www.amazon.com/Clover-Makers-...dp/B00579GQ7U/
The 1/4" and 1/2" are the ones I use the most. The Aunt Millie's vine looks like it might be a 1/2"; if not, then 1/4".
Alternatively, you can buy the Simplicity bias tape maker with assorted tips. I honestly do not see the need for this at all.
There are a few tips that make the Clover makers easier to use. One is to starch the fabric before cutting the bias strips. Another is to cut the leading edge at an angle to make it easier to get started through the maker. The first 6" or so of the strip are always a little wonky, so I allow for that and make extra. After getting the strip started, I simply make sure that I keep my iron close to the Clover maker so that the fold is pressed just as it is coming out of the tool.
If there are any small variations in vining strips, that is actually normal -- both in nature and in hand-made things. I don't mind variations and, anyway, they are so small no one but me typically ever notices them.
Here is a Youtube demo of how to use the tool:
http://www.youtube.com/watch?v=f-EkfTfjRFs
Hers would have gone better if she had starched the fabric first!