Add teabags to boiling water. Steep for 4 minutes; discard teabags. Add the sugar and stir to combine. Add the cold water.
Add the orange juice concentrate, lemonade concentrate, tea mixture, and bourbon or rum to a large (2.5-quart) freezer-safe container. Whisk to combine. Cover tightly and freeze for several hours or overnight.
When ready to serve, use a spoon or fork to scrape slush into glasses.