Could there be a second chance?

I dated my first girlfriend for a month and a half before she broke up with me for general reasons relating my lack of experience (ie I told her I "loved" her on the second date because I was too nervous to kiss her). 10 months later I've matured exponentially and I look at that break up as the greatest learning experience of my life. I seriously learned a lot from it, and I am very glad it had happened (though honestly I was not so glad at the time).

I did not know her very well when we dated, but now we're good friends and we hang out from time to time. Now that we know each other better and I've done some necessary growing I'd like to get back together with her. We really don't talk about our past relationship much, and whenever we talk I get the feeling that there's something on her mind that she's not telling me. I may be over thinking it, but it still bothers me nevertheless.

I want to know, is a second chance feasible in my situation? How can I bring it up with her? Any advice as well as opinions would be much appreciated.
Updates:
+1 y
We only dated for a month and a half and she did not say she loved me back. "stressed and burdened" very accurately describes her attitude after my awkward advance. I think she took the relationship serious (for a month and a half relationship that is).
Could there be a second chance?
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