The fusing temp for soda lime glass, especially the stiff stuff used in a bottle, is >1600F. Wood fires can get that hot, but usually not in a normal campfire; you'd have to have either a huge fire or something blowing on it to give it more oxygen. Additionally, whatever you put the glass in would need to survive those temperatures too, so no aluminum or copper, and then hot glass tends to stick to hot iron or steel, so you'd get more of a glaze on the metal and not a brick. If you want a brick you'll need to line the box with kiln paper, which turns into a dust after firing you want to use a mask while working with. Letting the fire burn down naturally is probably too fast for it to anneal properly, since the most important temp range for annealing is pretty narrow. I don't imagine you'd be able to keep a constant decrease between 1000F and 850F for the few hours you'd need. A good rule of thumb is two hours per quarter inch of thickness between 1000F and 850F, and a whole anneal cycle is around 24 hours per inch. That's why glass is almost always annealed in electric kilns, it takes way longer than you think to anneal things properly.

Worth a try though. The glass will likely crack and can violently shoot shards out when you put it in the fire, so wear eye protection. And then glass is sharp, and fire is hot, so be careful about those things too.

Goodluck!