I have been approached by at a guess at least 200 guys over the last 4 years. I am not exceptional looking, in fact I was bullied for being hideous - I just live in a high density city and tend to walk everywhere alone.
Some of those situations have been extremely uncomfortable. Do not be persistent. If she clearly isn't comfortable and is telling you she doesn't want to be talking/give her number, is even walking faster to get away from you: do not follow her, leave her alone. I really don't understand why 99% of men that I'm uncomfortable around don't see that there is no hope, I will only feel worse and worse about them the more they hound me.
There have been a handful of pleasant genuine conversations I've had when approached the street. I refuse to treat anyone unfairly - if someone comes and asks me for directions or talks to me I will treat them as any other human being. Sometimes I think they're a really genuine person who happened to see me and wondered what I was like - without being the kind to normally do that to someone and without only looking for one thing. Those people I will give my time of day, but I will never give my phone number... I can't completely trust their motives.
Only a handful are like that though, the majority are creepy, persistent, obviously using tricks/ploys/lies, degrading and dehumanising me, taking away my free will to decide whether I wanted to have anything to do with them because they already decided they wanted to be involved with me.
I've had horrible things said to me on the street for rejecting advances. I am always polite but firm, so as not to lead anyone on but also not to be unnecessarily rude.
Here are two opposite examples:
I fell asleep on the train. A man in his twenties woke me to let me know we were at the last stop, I thanked him and we both got off the train. He seemed nervous, quite sweet, he asked me where I was headed and I didn't mind engaging him in conversation. We walked for about 15 minutes talking, he was telling me about his job and a bit about his life, mentioned it was hard to meet new people and that I seemed nice and complimented my appearance. Eventually he admitted that he actually needed to go the other direction but had just been walking my way because he wanted to talk, and asked for my number. I declined as politely as I could - I can't bring myself to give anyone my number under the context that they are already interested in me romantically and I am not interested in them (I never feel attraction to someone I don't know).
This one happened just recently and really shook me up/upset me:
I had just been on a run, was in sweaty baggy joggers and walking back home. I had headphones on listening to music on a main road. A man approached me boldly and quickly saying things I couldn't hear, I thought he was just with some other people out on a Friday night for a laugh and show-boating in front of them by approaching me or something. I took my headphones off but still didn't catch what he was saying, he came right up to me into my space and asked me to come to his flat which was right there. I realised the other people weren't with him and had gone.
Me: No thank you, I'm going home.
Him: Where do you live?
Me: I don't want to tell you that.
Him: Where do you live?
Me: I don't...
Him: ... Where do you live? Where do you live? Where do you live?
Me: I don't want to tell you.
Him: Well just come to my flat then, it's right here! What is that? Headphones? *takes them from me and puts them on*
Me: Uh... yes... but, I want to go home now *takes them back*
Him: Just come to my flat!
Me: But I'm engaged! *shows ring*
Him: *looks annoyed*... Well... I live right here... *puts his arms right around me to hug me tightly and tries to kiss my cheek, I am pushing away as forcefully as I can*
Me: You can't do that to people on the street!
Him: Why not? Just come to my house.
Me: I am going home. *starts walking away very fast*
Him: *slightly aggressive tone shouting after me non-stop* THANK YOU, THANK YOU, THANK YOU, THANK YOU, THANK YOU, THANK YOU, THANK YOU, THANK YOU, THANK YOU *until I was out of earshot*
I don't even know what he meant by that, but it really unsettled me. I felt sickened when I got home. Most women have had similar unpleasant experiences on the street, on public transport, in shopping centres.... so you have to remember, they probably will be extremely wary of you.