Microwave water on high until steaming hot in a small bowl. Add tea bag and allow to brew 3 minutes. Remove tea bag. Stir honey into tea until it dissolves.
Combine berries, banana, and milk in a blender with ice crushing ability.
Add tea to blender. Blend ingredients on ice crush or highest setting until smooth. (Some blenders may require additional water to process the mixture.) Pour smoothie into tall glass and serve