Your approach might work if she has noticed you and is also interested in you. However, if she hasn't noticed you or she's noticed and isn't interested, then such a blunt approach is likely to make her uncomfortable, which will translate into her not wanting to continue the conversation.
What to do instead
A better way to approach is to find a less blunt conversation starter. Instead of just blurting out that you like her or that you think she's cute, start talking about something that she is interested in, such as the book she's reading, or another book from the same author, the music group/TV shows on the tee-shirt she wears, or the small dance she made. For example, if she was reading a book by an author you knew then you could say something like this.
Hey, I noticed you're reading [INSERT_BOOK_TITLE]. I think she's a fantastic author. How are you enjoying it so far?
You said in a comment that you don't read much and thus will be unlikely to know the books she has. That is perfectly fine. The important skill here is to make an observation about her that you can translate into a conversation that you know she will have some level of interest in.
What this accomplishes
I have a lot of experience (8 years of dating, 4 years as a professional consultant) with meeting new people and starting conversations. I've found that this is the best approach because it creates an active conversation for both parties. When you are attempting to meet someone that you like, it is especially important that they be actively engaged in the conversation, because if they aren't they'll likely get bored and move on.
This approach will be a lot more comfortable for her than simply walking up and telling her that you like her. Having someone that you've never met come up and express interest in you will take many people by surprise which instantly starts the conversation off at an imbalance (she'll be on her back foot so to speak because you've forced a romantic context into the conversation despite having never talked to her before). By starting with a neutral topic of conversation instead, there won't be an imbalance and she can be more relaxed and comfortable in the conversation.
This approach also has the added benefit of giving her the option to comfortably back out. As you converse, if she's not interested in continuing to talk, she can more easily end the conversation. My fiancee (also an introvert) has confirmed that it's much more comfortable to end a casual conversation than to turn down someone expressing interest.
