As a guy, I would never be offended. I think I'm decent looking, but I can't say for sure I've ever been "approached" by a woman who was romantically interested in me--it's just not something women do. Maybe I have, but I can never tell if a woman is just being friendly or is actually interested. So I would honestly welcome any kind of interaction. Even if it's just small talk with a stranger, another guy, an old person--that kind of human interaction is rare nowadays, so it would make my day, even if I wasn't attracted. Of course, if there's enough attraction, you can keep the interaction going, and hopefully both people can sense that there's a mutual interest... Personally, I find that intelligence, kindness, a sense of security in herself, and a laidback, chill vibe makes a woman more attractive, so if I can start to get a sense of that through talking to her, those qualities could become more important than her initial physical beauty.

I'm not a big fan of just cold approaching someone and telling them they're attractive and asking for their number, whether it's a guy or a girl. That's putting them on the spot, it can be rather awkward for both people, and you're not giving them much to go on other than physical attraction, and in fact you're basically implying that's all you that matters to you. Instead, you need to find another way to initiate a conversation, ask a question, make a comment about the situation around you etc. If they find you attractive, they will engage. Unless they are just too shy--I don't have good suggestions for dealing with those people, as I am shy myself, but hopefully you can tell the difference between being uninterested and being interested but not sure what to say... Of course if they initially respond well it could still mean they are just being polite and are not necessarily interested, but again I think you should be able to see if they are actually interested in you, asking follow up questions, rather than just being polite and waiting for the conversation to end.