Pour sugar into a 6- to 8-qt. pot and cook over medium-high heat, stirring often with a long-handled spoon, until melted and deep amber, 20 to 25 minutes. Carefully add cream (it will bubble furiously and sugar will seize up). Cook, stirring and scraping sides of pan occasionally, until sugar completely melts again, 10 to 12 minutes.
Remove sauce from heat and stir in salt, vanilla, and bourbon to taste. Let cool. Pour caramel sauce into a spouted measuring cup before pouring into jars. Serve cold or slightly warm (sauce is thicker when cold).
Make ahead: Up to 3 weeks, chilled.