Prepare the alginate bath by blending the sodium alginate into 500 ml of distilled water. Let the bath rest in a bowl for at least 15–30 minutes to remove any air bubbles.
In the meantime, prepare the peach mixture. Blend calcium lactate into the peach puree until fully dissolved.
To create the polka dots, gently drop small amounts of the peach mixture into the alginate bath using a small spoon, syringe, or dropper. As soon as two liquids meet, the drop is gelling from the outside in. The size of the drop will stay the same.
Let the spheres sit in the bath for about 1–2 minutes to form a soft gel skin. Remove the spheres carefully with a slotted spoon. Rinse in a second bath of just distilled water to stop the gelling process.
Assemble the Bellini by placing several peach "polka dots" into a glass. Depending on how sweet you'd like it, add raspberry spumante and finish with a serving of prosecco. Serve immediately to enjoy the fun effect of the carbonation making the peach dots to dance in the glass.