Combine the blueberries, water, sugar and salt in a small pot over medium heat and bring to boil. Reduce the heat and simmer the berries for 2 minutes. Remove from heat. Add the Earl Grey tea bags and steep for 3 minutes. Remove the tea bags from the pot.
Pour the mixture through a fine mesh sieve, a bit at a time over a bowl. Press the berries against the sieve with a large spoon to squeeze out their juices. Stir the vanilla into the blueberry Earl Grey tea. Let cool until safe to pour into popsicle molds.
Carefully fill your molds, leaving about 1/4 inch of room at the top as the popsicles will expand as they freeze. It's easiest and the least messy to use a jug or pitcher with a spout to do this. Wipe any excess from the top so that it doesn't freeze and make unmolding difficult. Add the popsicle sticks* and freeze for at least 5 hours or overnight.This recipe yields about 6-8 popsicles depending on the size and shape of your popsicles molds.
*If you prefer longer, straighter popsicle sticks to hold onto, freeze the popsicles without the sticks for about an hour or until they have started to freeze but you can still insert a stick to the depth you prefer and return them to the freezer. I recommend setting a timer because if you forget and the popsicles freeze solid, you won't be able to insert the sticks.