Partial mashing simply means that only part of the wort for the whole batch is produced from a grain mash. The rest is provided by either a kit or unhopped extract. If you use a kit, generally the grain mash replaces the kilo of dry malt or whatever you add to the kit. Extract with grains is usually pretty much all extract plus a small grain steep of something like crystal malt that doesn't require mashing.
BIAB is just a method of mashing grains to create wort. It isn't exclusive to all grain or anything. You can use it with a 19L pot to create small batches, create a smaller amount of high OG and IBU wort for dilution in the fermenter, or for partial mash beers, or you can get a 30 or 40 litre or more pot/urn and do bigger all grain batches with BIAB as well.
I skipped the partial stage when I made the switch, just went straight from extract and steeping grains to a 40L urn and bag set up to do BIAB all grain batches. Never looked back.