Adding store-bought orange juice to your bourbon will add sweet and tangy notes that complement the warm flavors. It will also make its texture thicker.
If you like the idea of adding orange juice but don't want the thicker consistency, you can dilute it with water or squeeze an orange straight into your bourbon.
It doesn't take a lot of orange juice to temper bourbon, and if you add too much, it may feel like you're drinking a classic sidecar, so don't be too heavy-handed.