To print Tasks in bulk, navigate to the Tasks > Pending Tasks page. Then access the drop-down menu and select 'Print'. Enter the date range of Tasks you want to print and additionally filter by User assignment and Task type if desired (leave as 'choose' for 'all'). Then select the version of printout you want at the bottom and click Print. Once opened in a new tab, print using your browser's built in print settings.
(Note even though the recording shown was captured within TheServiceProgramOnline, the process is the same for RouteStarOnline users)