As a pro bartender, under $10 per bottle is tough. I would go with the Barefoot brand. They do less expensive wine really well. Their Sparkling Moscato and Sparkling Pink Moscato are excellent alternatives to champagne.
You'd be surprised how good local brands could be. If you can do a tasting at their wineries, I highly recommend doing that. Boordy Vineyards, St. Micheals, and Hatteras are all favorites in the Mid-Atlantic area.
We bought a little over a case of 19 Crimes Malbec and it was a huge hit! The Santiago Station Savignon Blanc (drier) and Fetzer Gewurztraminer (sweeter) also went over well. All for under $10 per bottle.