Firstly, it probably felt uncomfortable to drive/ride a bike/tie your shoes at one point so dont worry about it being uncomfortable right now.
I find most women appreciate subtlety to start with, if they are keen they will follow your lead. Honesty and directness are very appealing but overwhelming for woman who are not comfortable.
Dont break up your conversation into 'teasing' ect. Your just talking to her to get to know her and because you found her attractive not because she is 100lb of meat you want to stick your dick in. You may say you dont want anything serious (ive said that) and you may mean it but you never go in with that wall in your mind it just creates distance between the two of you.
In terms of what to say i think if your listening to her, truly listening, you can pick up on things to talk about (to get to know her) and the opportunity will arrive. If you don't feel the opportunity is going to arrive you guys have been talking for a while and enjoying each other then go direct and ask if it would be ok to kiss her or say that you are really attracted to her.
An interesting experiment for you could be to just say whats on your mind as soon as you think it. Prepare for consequences though.
In saying all of that these are more my observations as im only really starting to put them into practice. so take it with a pinch of salt.
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if what is between me and where i want to be is sweat.. ill sweat. if its pain.. ill hurt. if its tears.. ill cry. if its blood.. ill bleed.
www.attractioninstitute.org/becauseifeltlikeit