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If she agreed to go backpacking with you, knowing you'll be alone together, I'd say she's at least interested a little romantically.
I wouldn't push it at all. Be nice, be funny, and just go into the trip without any expectations. Guys get weird when they think they might get laid. 2 weeks ago was at a house party, a few drunk guys were there hitting on a few girls, Jesus Christ it was uncomfortable, they thought they were smooth but were just downright creepy.
Don't be that guy OP.
You need to make sure she's comfortable. An air mattress I'd say is a must. If she's cold, and laying on the ground she won't feel much like kissing the tip of your penis. I'd avoid a foam pad. They are fine in a pinch but they're not very comfortable.
Bring wet wipes and TP for her, if she needs to go the bathroom make sure she's comfortable. I know my wife really appreciates having wet wipes just to clean up, even if it's just to clean her hands. Walmart sells little travel packs of wet wipes.
Not sure if it's your (or her) thing, but having a drink or 2 before bed is a nice idea. If she will drink liquor, a little flask of a sweet liquor would go a long way between you 2. Don't get her drunk more than a little buzz, a first time backpacker the next morning with a hangover is not a fun time.
Dating isn't easy after a long relationship. Sometimes it's hard to forgot what you learned over the last 4 years. I ended a 3 year relationship, and I made an executive decision to really keep an open mind. My new lady friend was nothing like my ex, and keeping an open mind really helped. 5 years later I'm married to her.
Pic maybe related?