The save system in The Bard's Tale Trilogy remains true to the original 1980s design.
To save the game (i.e. your character progress) you need to go the Adventurer's Guild and select "Leave the game" from the menu. Then it asks you to "Press <RETURN> to save all characters and end game play. Or press <ESC> to go back." Pressing the Return/Enter key at that point saves all your character progress and you can then safely close the game.