I have barrels hooked up to my AE network using AE Storage Buses. If I remove an item that is stored in these barrels using my AE Access Terminal, it removes a stack of the barreled item and puts it into my inventory. If I insert a stack of the same item, into the AE Terminal, it puts the stack into a storage drive, rather than the appropriate barrel. How can I fix this without using an Export Bus? The AE website explicitly states that Storage Buses work with both in-port and export, and that they are 100% compatible with Factorization Barrels.
There are two likely causes of your items getting stored in the wrong location, the barrels were not set as a higher priority than the storage drives (use the config tab on the storage buses to change the priority, the buses need to have a higher priority to ensure that the items end up in the correct location) and the system chose the drive at random, or that somehow an item of the type you want to store in your barrel got into the drive and the system is therefore (by design) choosing to fill up an existing storage location first.
Regardless of the underlying cause, getting all of the items to be stored only in the barrels requires that all items currently stored in the drives be removed from the storage system and then put back in in a way that makes sure they will be stored in the barrels, the easiest way to do this depends on the number of items involved.
If the overall number of items is small you can simply disconnect the storage bus from the network while pulling out all the items via the access terminal, then reconnect the bus and put all the items back in.
If you have a large number of items then you can pull the individual storage cells out of your network and put them into an ME I/O Port to pull items into the network with the only storage location available being the barrels.
That does not appear to be the case with the current version of the Direwolf 20 modpack The version of Factorization is 0.8.29 and the version of AE is rv14.finale3. The AE Storage buses are no longer able to ignore which side of he barrel they're attached to. They can only read an inventory if they are attached to the bottom of a barrel and they only read up to one full stack of the item. I don't know if this is an AE issue or a factorization issue, but it's not a user config issue as my system was working fine until I updated and my storage buses could no longer connect to the barrels.