If you do not have anything currently installed that is monitoring and logging then you do not have any way to narrow down which process(s) were consuming bandwidth. I would recommend vnstat or mrtg for overall usage statistics and nethogs for narrowing down which process is using your network bandwidth.
You can install all three by running these commands:
sudo apt-get update
sudo apt-get install nethogs
sudo apt-get install vnstat vnstati
sudo apt-get install mrtg mrtg-contrib mrtg-ping-probe mrtg-rrd mrtgutils mrtgutils-sensors pcp-import-mrtg2pcp
This will install each of the programs along with their associated modules and utilities.