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.
cooking.stackexchange.com/users/20069/razumny
I tried boiling the noodles with colored water and it didn't change the color at all.
I made a corn starch slurry with cold water (approx 1/2 cup) and McCormick's Colors from Nature (red 2 tsp), which is just concentrated beet coloring.
I mixed it into the drained, but hot pasta and came out with a nice pink color.
I finished it with extra virgin olive oil to help keep the noodles from sticking.
It's not as uniform as I'd like, and a bit dark in some areas, but it'll work for a Minnie Mouse themed pasta salad.
cooking.stackexchange.com/users/7820/cyberop5
I've tried dying pasta by just adding food dye to the boiling water, but you don't get very deep colors.
I then tried letting it sit in the (cooled) water for a while, but it really didn't get that deep.
(I didn't care about the texture as much; I needed something to use as intestines for halloween a few years back)
If you have the time, it might be easier to just make fresh pasta .
cooking.stackexchange.com/users/67/Joe
If you just happen to have a vacuum pump, you can try infusing the color similar to this article .
This method should push the color all the way through.
Otherwise, making it from scratch is the way to go.
This video explains how .
cooking.stackexchange.com/users/3649/MandoMando
I just saw a video where someone mixed the cooked pasta in gel food coloring , and it took on quite vibrant colors.
I suspect that the colors will then transfer to whatever the pasta comes in contact with (like your kid's face, if they're a messy eater), but it might be useful once in a while.
And in looking at the amounts he was using, I wouldn't be surprised if a pound of pasta required an ounce (2TB / 30mL) or so of coloring.
(although he was using a strand pasta, which has more surface area than bow tie pasta)
cooking.stackexchange.com/users/67/Joe
i added food coloring to my boiling noodles, turned out great!
very deep and fun!
cooking.stackexchange.com/users/39899/Crystal Hennessey
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?
How can I color pasta during cooking or afterwards, preferably using natural coloring?
cooking.stackexchange.com
<pasta><color><coloring>
cooking.stackexchange.com/questions/37995
cooking.stackexchange.com/users/2690/Jeff Axelrod
You can substitute some of the liquids with beetroot juice or add food colouring to the boiling or cooked noodles, or you could just make fresh pasta if you have the time. The method of coloring pasta depends if you are using fresh or dried pasta. Add coloured vegetables to the pasta dough for fresh pasta and use food dye or gel for dried pasta.
Colouring pasta is easy if you make fresh pasta. To color dried pasta, add food dye to the boiling water or food gel to the drained pasta.