You don't need to even cover the bucket, except with a towel or something to keep out fruitflies so don't worry about the headspace. Stir it up a couple of times per day to re-submerge the fruit and "smoosh" the fruit up well. Then, transfer when the wine is about 1.010 and airlock it at that time. That's when you want to protect it from oxygen.
Sometimes it gets to .990 really fast, so I miss the 1.010 window, but it's still always been fine.