Things like: "You know, a lot of people might be offended by someone trying to make friends (NOTE: Do not use the words "pick-up") with a stranger in public. But really it is just like meeting someone at a party," and" I like to think of it as a self-introduction. And why not? If you are impressed or attracted by someone, why shouldn't you come forward and say so?"
And "I've been around this area quite a while and I've noticed that people are a lot more casual in their way of talking to people. I mean, things are more open now. I suppose it is the permissive society we hear so much about." You should memorize the gist of some of these “filler" lines, or others like them. You probably can think of plenty others yourself.
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A few good filler lines that give you at least a weak additional excuse for stopping the girl are:
"Well, I just like to meet new people."
"You know, this is a good opportunity to meet new people," (beach, sporting event, or any occasion).
"I just like to talk to interesting people." (Then tell her why she interests you.)