People associate shyness with low self confidence - which is a huge turn off to woman, often subconsciously.
You're gonna have to fake it, unless your looks are good enough to carry you.
Rather than using the word 'shy', go with 'reserved' and make it out like you're 'reserved' by choice.
Like instead of advertising the fact that you're scared of woman, just make it out like you don't go on many dates because you're extremely selective and are holding out for someone who really interests you.
This way you're able to get your point across without coming off as undesirable.
Here's another example of how you can restructure your anxiety into something that'll make you look good...
Sometimes on dating sites a girl will hit me up and she'll be extremely straight forward, asking for my phone number and wanting to setup a date right off the bat. Now of course I'm intimidated by this aggressiveness and there's no way I'll be able to make such a huge step without first getting to know the girl better. I need talk with a bit more via email before my comfort levels will adjust.
So what can I do? If I tell her the truth, it'll put her off and she'll lose interest. So instead, I reshape my anxiety into something that actually makes me look more desirable...
"Hey, so the last girl I met off this site turned out to be a little bit psychotic and ended up stalking me haha. So now I'm sorta taking a more cautious approach. You seem pretty cool though, care to tell me a bit more about yourself?"
Sounds silly but it works.
