A good solution that @wilf and I found was to install obexpushd, a daemon that will accept incoming OBEX (and therefore Bluetooth) file transfers and save the files to its working directory.

Just apt-get install obexpushd, and run it in the directory you want the files to be saved in. Or, if you'd like it to start with your machine, here's a simple Upstart job file that should do the trick:

chdir /home/USERNAME

exec obexpushd -n

start on startup

Save the above as /etc/init/obexpushd.conf (making sure to change the first line to point to the directory you'd like the files to be saved), run initctl reload-configuration, and start obexpushd.

Once you've paired your Bluetooth device with your machine, you should be able to send files to it without having to manually accept the transfer.