To dye for

There's some white sock yarn, 75% wool, 25% acrylic or whatever, in my stash that I bought ages ago. This yarn is longing to be dyed. Right now I happen to have a couple of beetroots leftover in my fridge, and as K is still on holiday I'm not likely to eat them; I'm just not a great fan of beetroots. However, as I know the color of beetroot (my family are beetroot-lovers. My mom always makes a salad, and I know what her lips look like after such a salad), I thought it might look nice on the yarn. I haven't dyed anything apart from easter eggs before (here, it didn't matter if the color didn't stay on long), and I don't want the color to wash out (too) easily. Is there a way I can make the natural color stick to the yarn without washing out? Do I have to add chemicals, or is there a natural way of dyeing? I heard that back in the olden days dyers would use urine to help make a good color, but I don't want to be this natural. Is there anything I have to pay attention to while dyeing? Or am I just insane, wanting to use natural dye (or dyeing in general)?