Last winter break I was seeing this girl who I was hoping would be more than a friend. I did so many sweet things for this woman. We did the usual thing a casual couple does...go out, mess around, blah. Well, turns out she didn't want a relationship. Sometimes when I would open the car door for her or bring over a thoughtful "present" (like her favorite candy), it seemed like she appreciated it, but it pushed her away. At least I knew where she stood at that point.
You really have to get a feel of what this girl wants. While bringing a flower might be considered a meaningless thoughtful action, she might analyze that as "omg, this guy is taking "us" seriously." She might put up an emotional wall and run away from you. On the other hand, if she's interested in the same, she might choose to get closer to you.
When in doubt, do what feels right. If she's into you and you want something to come of this, give her something playful (sunflower or tulip is perfect). I think it would be too early for a rose. This way you get her on the same page as you, even if it's for one night.
Oh yea, if you give her a tulip, get 6 of them. Keep the dates fun and casual...be yourself and act natural...