The most natural route would be to pick the bugs off when you see them, spray with a strong spray of water. If it continues you could spray with Neem Oil, Alcohol, Murphy's Oil Soap, Safer's Soap, and I'm sure there are more options out there.
There is also quite a bit of information on companion planting..... I haven't figured that part out yet. Good Luck!
Here is a site that I like to go to, for reference and products.

Well, I don't know if it will work yet since I haven't tried it, but Smith's Marketplace in Logan had organic pest control sprays on clearance (marked down from $15 to about $1.50). One was had peppermint oil, another had fish oil or something. They say to spray weekly. I'll have to post to let you know if it works or not once I start spraying. I figured that it was the right price for me to try using it.

Maybe someone else has experience?

First I would refer you to utahpests.usu.edu. That is the most comprehensive website that I know of when it comes to pests or diseases. As for natural remedies, I prefer organic pesticides such as BT (brand name Thuricide). BT is a pesticide that is naturally occurring bacteria that will not harm beneficial insects such as bees or ladybugs, but if sprayed frequently, it will kill most worms and some other bugs. Chemicals such as these are described on the website above. I have posted a picture of the chemical BT on my blog.

http://www.vegenag.com/2009/03/pest-and-disease-management-for-the-backyard-vegetable-gardener/

Before spraying I would verify that it is some kind of insect. My experience, especially with the cabbage family is snails and slugs. I have all my beds ringed with a copper cloth from Lee Valley and no problems. And good organic soil helps too.