First, never stir. A gentle swirl is fine, but aggressive mixing will flatten the drink. Second, don’t skimp on the wine. A $8 bottle of Cava will work, but a $15 bottle of a decent Crémant will taste noticeably smoother. Third, consider the glass. A thin-rimmed champagne flute is ideal; it keeps the bubbles concentrated and the aroma focused.
Here’s a fun fact to drop at your next party: The Mimosa is the most popular sparkling wine cocktail in the United States. It outsells the Bellini (which uses peach puree) by a wide margin. Why? Because orange juice is a universal comfort food.