We recommend you Uber, Metro or walk.
If you decide to Metro, the stop closest to District Winery is Navy Yard-Ballpark on the Green Line.
Yes - if you prefer to drive you will be able to park nearby. The most convenient parking option around the Winery is an open-air, public, pay-by-the-hour lot called Lot Q on the corner of 4th & Water Street just behind District Winery. Rates vary day to day, but generally fall between $3-$5 per hour.