I have made ginger beer from my own "ginger bug" but did not get much carbonation. I think I put it in the refrigerator too soon, so I took one bottle out, let it sit for 2 days and VIOLA, carbonation is perfect. Question: Will my ginger beer still be okay (safe) for drinking if I take the bottles out of the refrigerator, let them sit for a couple days and then put them back in the refrigerator?
It will be absolutely fine. Drink and enjoy.
By dropping into the fridge so early you just caused the yeast to stop their work. By removing it and allowing it to warm you have restarted the fermentation. You could happily leave it out of the fridge for a few months and so long as the bottles can handle the pressure that could build you would have no issues. It won't go bad from sitting out of the fridge.
I leave mine in the shed for weeks and it can get very cold and then the temperature goes back up. Its fine once your bottles were very clean before bottling. Any type of mold is what you need to avoid in the brewing process. If you were making elderflower champagne you'd be leaving it for 2-3 months, so what you are doing should be fine since the process is very similar.