I've only known her for about a month now and when we talk we seem to share some of the same things in life.

We are both kind of busy and haven't been out on a date yet but I wonder I should ask her on this 6 day trip with me to break the ice or not.

I can't really tell if she's intrested in me or just being polite.

Part of me says"Yea go ahead and ask" the other part says"She might think i was some kind of nut" What do you guys think?

By the sound of it, you really like her. I have been in this position more often than not, and from personal experience, my advice is to go for it!
The worst she can say is no! If she does say no, be cool, don't get angry or upset, because she'll respect that.
Ask her in an offhand way if she wants to go for a walk or something, but if you think this way won't work, then mayb just start a conversation, and ask something like 'u doing anything this weekend?'
Good Luck!
Addi

WOE There! Take it from a girl... don't ask her. I'm sorry but, u'v only known this girl for a month... and you want to take her on this 6 days trip... first-she mite think you're only in it for the .. u know... 6 days... 5... NITES... so be careful if you aaare going to ask her, so she knows your intentions are only to get to know her better... mentally. But it is a little forward if you've only known her for a month... hope I could help. One.

Yea, but if he's known her for a month! Surely that's reasonable to ask her to go on a trip! If you just treated her like a friend first, just look for signs... or ask one of her m8s to ask her if she likes u...
Good Luck anyway!

I have to agree, wait after the trip is over then ask her out to the movies or something