So how was her reaction when you asked her whether she had opened it? Did she realise she had made a mistake, was she apologetic about it?
It could have been an honest mistake. Quite a misjudgement on her part, maybe, but still, not with evil purposes. She might not have realised it was a specific hostess gift. And she might very well not have realised how expensive it was. For some people, a bottle is just another bottle.
To be honest, I am a little iffy about bringing a bottle of exclusive champagne as a hostess gift to a BYOB. That just seems a bit of an odd thing to do, and could very well lead to confusion.
This being said, to answer your question: no, when a guest brings a gift for the hostess, the other guests do not have the automatic right to dig in and share. But I'm with Toots that it would have been better to put it further away if you wanted to save it, out of sight and out of reach, to avoid confusion.
Lastly, a question: are you really sure she drank it all by herself? She says she only had one glass. You said yourself that you were too busy to see her open it, let alone drink it. Would you have noticed if other guests drank of it, if you didn't notice that she drank it? Maybe it is not completely fair to assume she drank it all by herself.
I hope this gets resolved in a way you are both comfortable with, because in my book, a bottle of champagne, no matter how expensive, is not worth starting a neighbour feud over.