This girl that has been staring at you for a while and got nervous when you approached her may have been really uneasy with the manner in which you approached her.
Being that you approached her in a very crowded place, she may not have even been entirely sure that you were the same person that she has been staring at for the last 25 days or so.
It may be best to approach her in a way that keeps her from feeling defensive or uncomfortable.
Since you have noticed that she goes to that coffee shop everyday with her friends, it may be best to plan on a day that you will be at that coffee shop as a customer.
In essence, plant yourself there before she arrives with her friends.
Make sure that you are in a visible area of the coffee shop where she will clearly be able to see you.
Once they have settled and are enjoying themselves, you can make your approach.
Being that you are already a customer in the coffee shop and she has had some time to notice you sitting there, there is a higher likelihood that she will be a lot more comfortable when you approach her this time around.