Speaking of this matter, I have this one friend who is a flirty, aggresive and outgoing type. She will try to approach (in a soft way) any guys she finds attractive and I do admire her confidence. I'm in a relationship so I don't approach guys but if I was single, I am not sure if I can be like her. Oh the result of her approaching guys is POSITIVE. Most guys responded well.
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A girl who is at least moderately attractive physically and who has a fun, friendly, sweet attitude is going to generally have a positive response from men. However, you probably can't just approach a man and ask him out - that's so rare for most men (it only happens regularly to men who are 9+) that most guys would be suspicious. Now, if a girl comes up and starts a conversation, and 20 minutes into it she asks the guy out, she's almost always going to get a yes if he's single and looking to date.
I would encourage the behavior. Remember all you are doing by making the 'first move' is communicating clearly to a stranger that there is something you find attractive about them or that you want to get to know them better. If a girl did that for me as has happened previously I would feel flattered and return to advance by talking to her and seeing if we have anything in common. I would take the lead at that point in asking her out on a 1st date and planning it, but hey if she likes me initially I am all for it. I don't see the gesture as being desperate because I know that I am a catch and know she will need to earn my trust and attention through the dating process.