While waiting in the second fermentation, don't cap the bottle with a lid. Instead, put a balloon over the top of the bottle. The balloon will expand without letting the carbonation escape. When the balloon starts to shrink, then put the lid on. Hope this helps.
I am attempting this now. I have a question about the bug - can I re-use it after straining? Or do I have to start the bug fresh every time I want to make this?
If you continue to re-use the bug, can it eventually become a "ginger beer plant"? I would think re-using would speed up the initial fermentation so you are ready to bottle quicker.