Starting conversation with gym mate?

So I recently joined a gym almost 1 month ago near my house and there's a really pretty girl I am trying to talk to for several days but I can't think of anything to keep conversation going after 'hi' 'hello'. And that's because I am an introvert and this will be my very first approach to any girl. Also she maybe 2-3 years older than me and workout alone. So as I said I am an introvert but I am confident enough to keep up a good conversations, I just don't know how to start. So, I was thinking that maybe I draw her a nice sketch and give it to her after gym (I have good hand for sketches). It's just that i don't want to look like a stalker or a desperate person because we have never interacted before and suddenly this might be weird for her. Please suggest me something. Will this be ok? What would you ladies do if someone suddenly gives you an sketch like this. And I am not thinking very far for now like any kind of relationship I just want to talk to her like a friend.

Starting conversation with gym mate?
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