You can bulk assign members using the 'quick action' feature at either the grid or element level.
For bulk actions on all tasks across all elements use the grid task log.
For bulk actions on tasks in a single element use the task log in the element.
The feature functions the same way regardless of the task log you are working in (grid or element). Depicted with a lightening bolt, the 'quick action' button (visible to architects or any user with edit/manage rights to a grid) when clicked displays a new set of selectable circles replacing the task checkboxes and two other buttons 'Assign' and 'Schedule' located next to the 'quick action' button.
Select some or all of the circles alongside each task row (you will see a bolt appear in the circle when selected) and then click 'Assign', an off canvas window will appear on the right of the screen with all members who have access to the gird, simply select a member to assign them to the tasks you have selected. To unassign, just click on the 'Unassign all' link in the off canvas member window.
This will update across the element, the grid and any assigned users 'My tasks' dashboard.