Bear in mind that if you sparge, the wort you collect from the bag after the sparge will be fairly low gravity, probably not high enough to make a decent starter.
As for how long the starter wort is safe when refrigerated, I just brewed a batch yesterday and used a starter that was reserved from a brew on 3/27, that's 4 months. The starter took off well and the batch is bubbling nicely, we'll see in a week or so whether it is good or foul. When reserving wort for starters or kraeusen I always boil the wort and pour it at boiling temps into sterilized 1/2 gallon juice jugs, put the lids on, turn them upside down and chill as quickly as possible in a water bath. I'll watch here for others with more knowledge and experience to explain what I am doing wrong, and why it's not a good idea.
From my limited experience BIAB is the only way to go, at least if you have a good quality bag.