Put the bottle in a smaller container of clean water inside the larger container of water with the top sticking out of the water so it doesn't overflow into it.

Put the bottle in a smaller container of clean water inside the larger container of water with the top sticking out of the water so it doesn't overflow into it. It'll take longer to boil without the convection but you'll get there eventually. You can fashion tongs out of sticks to pull rocks back out after their heat has mostly transferred to the water while you put newly heated ones in.