I avoided navy for years, so I understand. I think for a long while, navy seemed like a color used in conservative, traditional style, and I associated it with nautical looks and very preppy or corporate looks, which are pretty much at the opposite end of the style spectrum from me.
I appreciate navy more now, but I still can count my solid navy items on one hand -- a Theory moto jacket (which is actually so dark it might be more of an ink blue), a pair of casual linen pants, and a sleeveless blouse... I am starting to appreciate more items with navy as a base for prints, and have a couple of blouses and a skirt that have a navy base rather than black, and I enjoy them. They seem to look particularly good with white bottoms and jeans.
Maybe if you find a print with navy that really appeals to you, that might be a way to ease it into your wardrobe.