[theorique]

Usually, if it's going well, I'll tell her I'm there by myself, and they tend to be impressed I had the confidence to go out by myself and approach them.

Absolutely. People follow your lead.

If your manner suggests that you're ashamed of what you're doing, or that you think you're doing something 'wrong' or 'awkward', they will believe that.

If your manner suggests that you're engaged in the most normal activity in the world - being friendly as a human being, going out and interacting with other human beings - then you will put others at ease and they will be comfortable and friendly around you.

Now, that's not to say that everyone will think it's normal. But that's OK - people who find your behavior objectionable or 'strange' are probably not a very good fit as a friend or a lover.