Open an elevated command prompt and execute netstat -a -b. This will list all executables currently connected or listening on a port. It is not uncommon to find over a hundred entries, even when you're not actively using your internet connection. Most of these are not consuming large amounts of data. Measured over several hours, 300 MB of unidentified traffic is not normally worrisome, but sufficient to expect the culprit is easily found.
You can monitor how much bandwidth a process uses from Windows itself on the Network tab in the Resource Monitor, opened with resmon or via the Performance tab in Windows Task Manager. The first list, 'Processes with Network activity', shows time-averaged numbers of bytes used per second for individual processes. I am unaware of a built-in feature to monitor these figures over longer periods. If the process does not immediately reveal itself, you would have to keep an eye on it.