To me, BYOB means that the hosts are not providing booze, and if you wish to drink an alcoholic beverage, you supply it yourself. True, people do share, and mix and match, but I don't think it would be cool to drink other people's alcohol without bringing some yourself to share. As a PP said, that would classify you as a moocher, even if there is a glut of alcohol other people have brought.
What I do if I want to have an alcoholic beverage at this type of party, but I'm too broke to buy a lot of it and leave it there, is I buy a single serving size beer for myself, or I team up with another person who is going to share a bottle of wine. I avoid buying a six-pack as I usually end up drinking one or two and leaving the rest there, as it feels tacky to take it home with me again. So I buy only what I plan to consume.
If you're thinking of a nice bottle of wine as a host/ess gift, that's another matter. It would be a nice gesture, since they are providing a lot of food, but that is separate from the BYOB issue. You could bring them some flowers or something.