Prepare an ice-water bath; set aside.
Place milk in a medium saucepan and bring to a boil over medium heat. In a medium bowl, whisk together egg yolks, sugar, and salt until thick and light. Slowly pour in half of the hot milk, while stirring constantly. Slowly pour the egg mixture into the remaining milk mixture, stirring constantly. Stir in bourbon.
Place saucepan over low heat and bring to a gentle simmer, stirring constantly. Continue cooking until mixture is thick enough to coat the back of a spoon and reaches 180 degrees on an instant-read thermometer. Remove from heat.
Strain creme anglaise through a fine mesh sieve set over a medium bowl. Set bowl in ice water bath and stir creme anglaise until cooled. Keep refrigerated until ready to use, up to 1 day.