BigCommerce Connect 3 can update Inventory for BigCommerce Products in real time. Upload one time, and BigBusiness will get the BigCommerce ID for posting new Qtys.
In Connect Settings for BigCommerce choose Link-Only for Update Products. Then, in Items Search select some items and click Upload. Wait for Success! and you're set.
Once the BigCommerce ID is set on the Item, any change will update BigCommerce. This uses Auto-Connect, Update Availability, and Update Product Pricing settings.