the first thing is, why does she go out with you? is it just because she wants to have a boyfriend? i am asking this because i don't think anyone can recover from the last relationship so fast and start dating another person so soon. before you two go dating, she should have know that you are shy sometimes. if she really loves you, she should tolerate you personality. i don't actually think it is your problem. if she wants to talk, she can start a topic to chat but not complain.
but of course, if you want to change your shyness, i guess you can talk to her about her daily life, like what she is doing recently, any special things happen, etc. or you can tell her things happen around you, better if they are funny so the conversation will be happier. if you don't have courage to start a topic suddenly, take her to a movie, and after the movie ask her about her thinking and feelings towards the movie. then you relate things she said to different topics. so the outcome will be you have a lot to talk about but you don't have enough time.^^
i hope this can help, but i really think you should figure out why you two are together.