There are no bars at Volubilis — the site is in a rural area near the sacred town of Moulay Idriss, and alcohol is not available in the vicinity. The café at the site entrance sells mint tea, coffee, soft drinks, and water.
For a café stop, Moulay Idriss has a few simple cafés on the main square where you can sit over a glass of mint tea and watch local life. They are not set up for tourists and menus are rarely in English, but they are welcoming. A glass of tea after the walk around the site is one of the pleasures of the combined visit.
If you need a cold beer or a glass of wine after a hot day at the ruins, wait until you return to Meknès, where hotel bars and licensed restaurants can oblige.