Hello TexasAndy, and welcome to ChefTalk. You need to use milk instead of water to get a really nice white color.
Here's how I make it using 1 coffeecup of rice;
Use round rice like Arborio. Measure 1 coffeecup of rice and rinse it in a sieve. Bring 5-6 coffeecups of full fat milk to a simmer, adding 1 split vanillapod (scrape out the seeds but add the pod too). Add sugar to taste. Sprinkle the rice in the simmering milk and add a tbsp. worth of good butter which will prevent the milk from boiling over and give an extra taste. DO NOT stir the rice during the whole cooking process. Let simmer on low fire, lid on, for as long as it takes to absorb all the milk. When done, leave to cool entirely, preferably in your fridge. The rice will now be a very stiff mass.
Measure a coffeecup of liquid cream, add a little sugar and whip to a semi-dense consistency. Gently fold the cream into the rice. From now on the rice will remain fluffy, even when it comes out of the fridge.
Here's a few examples;
I used saffron in this one, so you get a yellow gold color. Just leave it out to get a nice white rice pudding.
Here's a white rice pudding topped with a little grated chocolate