The best way to do this is to SSH into the instance and use the gsutil command to copy files directly from the GCE instance to a GCS bucket.
Keep in mind the instance needs to have Google Cloud Storage "write scope" which is a setting you need to create when you first create the instance OR you can add later using a service account.
If you're using a machine image that was provided by Google, gsutil is already installed on the VM instance.
Example:
gsutil cp file1 file2 gs://bucket If you have a lot of files to upload, you can parallelize via -m:
gsutil -m cp file1 file2 gs://bucket If you want to recursively upload a directory, use -r:
gsutil cp -r dir1 gs://bucket See the docs for gsutil cp for more information.