Is it ok to ask a classmate on a date?

EDIT: Had to change title to make it more descriptive due to fluther mods, so if you replied to this I never got to read them.

Ok there is this cute girl in my class who has my attention. We have class twice a week and class has been going on for about 3 weeks now. We talk, we do our work together, and she seems interested (telling me random details about her life, job, etc and laughs).

Would it be somehow wrong or create a conflict of interest if I asked her out? Something simple like at the end of class:

Hey, whats your plans for tomorrow?
....
Ohh, well I’m going to see Legion tomorrow, want to come?

I’m just getting really tired of having women come around me and I feel like there is something situational to why I can’t act on it. Thoughts like, “Ohh we haven’t known each other long enough.” “She’s in my class”, “She’s my friends friend”, “She’s already been claimed”, “Sbe’s too close to my social circle.”, “She chills with frat kids.” I always let women who seem intrested in me at first get uninterested in me due to failure to act. ALWAYS!!

I want to just act on something already. Is this wrong? Is it wierd to ask girls in class out? Will this create a conflict of interest and will there be something “wierd” for the rest of the semester? Is it too soon to act? Am I over thinking this?