Make each of your fruit purees separately. For example, start with the strawberries. Add the strawberries to your blender and blend until pureed. Taste the puree to test its tartness, then add in 1 or 2 oz of simple syrup (depending on how sweet you want it, or how water-dense your fruit is – FYI, my blackberries needed more syrup/water than my strawberries b/c the puree was thicker and more tart) and blend again.
Pour completed mixture into a glass or jar, and set aside.
Rinse your blender and repeat with the next fruit.
Store the fruit purees in the fridge until you are ready to serve. (Shake or stir the puree if it begins to separate)
To serve the bellinis, add some fruit puree (as much as you want) into the bottom of a champagne flute.
Top it off with prosecco, stir, and serve.