I remember a few years ago at this gathering, there was this woman with a socially awkward husband. She would be chatty and lovely and stand by his side, and she did the same thing with me. She approached me and talked a bit, then stood with me and didn't talk so I could approach her if I wanted to. I knew it was "safe" to talk to her because she began conversation, then stood by my side adjacent to me i.e. faced away from me, but not totally. She also didn't look directly at me. It made me feel comfortable.
I think the main thing was that she was completely OK with me being silent, she didn't take it as rudeness and she didn't feel awkward about it, and didn't speak about it. It made me open up.
I think you have to be totally OK with the shy person's presence, otherwise they will sense the awkwardness and clam up. I mean, I might not have got what this woman was doing before I studied body language, but she was definitely open and friendly to me, and adapted to me. I don't see many people do it.
So yeah, bottom line my advice would be to approach them and talk a little bit to them, and stand with them. If they keep looking around anxiously for ways to "get out", then calmly walk away. Or they might become less animated in body language, in which case again, walk away. Otherwise, just stand with them, then let them approach you.
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I've left WP.