There are as many approaches to BIAB(bag or basket) as there are brewers. I haven't ever heard of anyone doing what you describe however. Dipping the bag/basket back into the wort probably wouldn't net much better efficiency and would only serve as a mashout if you wanted one.
I use two vessels to BIAB because I like to do a sparge. I mash in the kettle with a bag and fairly typical water to grist ratios. When the mash is done I pull the bag and leave it suspended over the kettle I run mashout temp water over the grain bag until I get my preboil volume in the kettle. I tend to get great mash efficiency this way.
I think the majority or BIABers tend to do a full volume mash in one vessel, pull the bag/basket and boil. Your crush will play a big role in what kind of efficiency you get if that's your process.