I know that compass headset caps are available. I've never used one so I can't comment or recommend or anything, but that's what I would do.

I wear an ABC watch, so I feel like I've got it covered. It's harder to look at on the bike, but I'm also a hiker and skier, so in my case it's a good tradeoff.

If you felt like going the watch route, Suunto's Core watch is excellent and the battery is good for a year.