Currently any parent sku of a bundle doesn't automatically relay fulfillment sync back to Shopify.
Our work around is to copy the tracking for the package and manually fulfill these line items within Shopify.
It would make a huge impact to the daily operations saving us hours of manually fulfilling orders within Shopify especially if the company scales and adds more and more bundled products.
If it was possible to treat the parent sku as a fulfilled line item I believe this would fix the issue but currently I believe only the child skus send fulfillment back.