How can I turn my muffin batter into the natural blue color from blueberries?
The story is more complicated than SAJ tells it. Blueberries, like many other purple foods, are colored by a pigment called anthocyanin. It changes its color from red at very low pH to real blue at very high pH. At the blueberry's natural pH, the color is a purple with more red than blue in it. 

What you can do is to juice some blueberries separately, then add lots of baking soda to the juice. It will turn a dark blue. You can then mix it into the batter. 

The problem is that you will be changing the taste of the muffins, and some of their rising behavior. If you use little enough blue-turned juice to not make a major change, you will get dirty greenish muffins, as the batter itself is yellow-beige, and that will mix with the blue. If you use enough to color them, you will have pretty display muffins (provided they don't stay flat because you turned the batter too alkaline for the baking powder to work) which will taste like soap. 

Personally, I will stick to food coloring. "Natural" coloring is an unachievable utopic for most foods, as natural pigments are finicky and almost never concentrated enough to color a food flavor with them. The only time they work is when a food is made predominantly from the coloring food, e.g. blueberry sorbet is indeed red-purple from the blueberries contained in it. 



This is an example of naturally colored shortbread cookie dough. The lavender dough was colored using elderberry fruit juice with lots of baking soda. It was very noticeable in the taste, I wouldn't do it again. Ironically, the slightly soapy taste fit a bit with the lavender aroma, it was just weird eating the stuff.