Need advice regarding after eye contact

Just wondering if I can get help please on some suggestions

There’s a couple of girls I like and have made good eye contact with and smiled but that’s it
Should I just say hi, how are you? Then ask if they want to swap numbers?

More recently I got speaking to a girl at a bookmakers, on the horses and I asked who she had put on the she asked me but that was it . how can I have progressed that kind of thing?

I’m quite a quiet shy guy and my type is the shy/quiet type

And I am not sure on really what things to say in general after making eye contact and smiling.
How can I progress it e.g starting a conversation then like making it flow

I know it depends on circumstances but I don’t feel I’m getting anywhere

Thanks, any help would be appreciated.

Hmm, hi.
This would be a hundred percent opinion. For me, as a girl. After an eye contact i expect the guy to come over and say hi. But if not. That's just it.
To make the conversation flow i would suggest that you make a thing go big. Just like you were in a store, get the thing you want or attracts your sight and ask if she likes it to, if not ask her what does she like. And when you get the convo, just slip in the swapping of numbers. for me the personality is the point before giving my number. A:d if course when you got the number you would do the first movd. You never know the girl must've been waiting your call.
Well, that's all i guess. Hope i helped!

I don't think he would just go into a girl and say: Hi, what do you like?
It would not be natural.

Just go over her and make it look like it's natural. Find an excuse why you go and talk to her.

Ex: Hello, I notice you are in my Math class, I am having hard time with it, can I count with your help? And it flows.

If you had the extra confidence you just would go there and tell her that she caught your atention, the way she acts. But anyway it's all about creating chemistry because the first impression is the most important

Good luck mate