How can I color pasta during cooking or afterwards, preferably using natural coloring? My daughter asked me if I could make her red bowtie pasta in honor of Matt Smith as Dr. Who.  

I'd rather not use an artificial dye.  Either way, how would I go about coloring the pasta itself? Assume that I am starting from store-bought dry pasta. Would I have to add the dye to the water in large quantities, or would adding some to melted butter and tossing work?
You are not stating whether you are making the pasta yourself or if you are using premade pasta. I am going to assume it is the former.

For red pasta, I would recommend substituting some of the liquids with beetroot juice. You will need to experiment with it to get the color right.

I would also recommend trying it in pasta both with and without egg, as the yolk will play a role in how the color develops.