Hey, the bugs PROVE that you grew the spinach organically!
But it can get kind of gross, I know. What I do when I gather greens (chard, kale, spinach, bok choy, broccoli, etc.) is to soak them in a sink of warm water with a couple of dashes of salt. The warm water opens the pores of the leaves so that any soil falls into the water, and the salt makes the bugs unhappy so they leave the veggies.
Then I lift the leaves out of the water, letting the salt-infused water drain out of the sink. It's amazing, the crud that *can* be left behind sometimes, esp. if it's been raining recently.
Then I run a second round of water, cool or warm, no salt, and plunge the leaves up and down a few more times. Lift leaves, let water drain, proceed with dinner preparations.
Welcome to gardening, and to this forum.
Sunset Zone 17, USDA Zone 9