There are good biological reasons why women are more choosy than men (size of investment in child rearing), but as you say, most people do end up in relationships, so it typically means men have to do the most work persuading women of their desirability, and many women end up partnering with men they wouldn't have considered based on initial impressions.
Be the mysterious woman having fun.
A man's imagination is far more powerful than any reality you might conjure up, you can reveal too much.
Remember, men will consider 90% of women, but women only consider 10% of men.
There's a lot of competition for that 10%.