As part of its upload process, the Bulk Uploader addon writes files to a couple of different locations on your server. For this to work correctly, these folders and their contents (including any subfolders) should be write-enabled for the user running the PHP process:

addons/bulk_uploader/uploads/
addons/bulk_uploader/tokens/

When in doubt, CHMODing these folders to 777 should do the trick. 755 should be sufficient for servers running SuExec, and Windows-based servers should un-set the Read Only flag.