The result:
If you are operating on a dataset that is fault tolerant, or doing a one time process you can verify, changing WriteAcknowledge
You can try to modify the Write concern levels. Obviously there is a risk on this, as you wouldn't be able to catch any writing error, but at least you should still be able to capture network errors. As MongoDB groups the bulk insert operations in groups of 1000, this should speed up the process.
W by default is 1:

When you change it to 0:

If you are not concern about the order of elements, you can gain some speed calling the unordered bulk operation
await m_Collection.BulkWriteAsync(updates, new BulkWriteOptions() { IsOrdered = false });
With an unordered operations list, MongoDB can execute in parallel the write operations in the list and in any order. Link