I'm not single but have been for a long time and really regardless of relationship status, approaches like these work out best when they are casual. Don't spring a whole show and dance upon someone, but make yourself known to them as a cool and maybe kind of funny person who is curious about them and likes their vibe. It is flattering for someone to be into you, especially when it feels like it's not just your looks/figure/face but your person.
Yes a lot of people might be kind of in a hurry or in a different headspace or taken or whatever. That doesn't matter. What matters is taking your cue for when to leave. If she avoids eye contact or gets out her phone, gives short answers, doesn't ask questions in turn, wish her a nice day and carry on. Save all your energy for girls who give you something to work with, whether that's smiles and active listening, or telling you about themselves and what they like.
If you really like someone and want to bond with them, it greatly helps to go some place together. Even if it's just accompanying each other to the spot where only one of you need to be and parting there.
Don't go on tangents about your beliefs or your life. Work in snippets in comments, anecdotes and jokes. Work your best angle. If you're (for example) not a funny guy, don't try to be, just work on being good company in different ways. Don't overanalyze how a single girl responded to you, look for patterns between experiences with different women if you want feedback from your experience.