Bane in Dark Knight Rise wears a mask to hide injury, and there is no mention of Venom.
Bane in the comics wears a mask because it's what all the cool guys are doing, and he receives his strength through the Venom formula.
Bane in comics likely eats normally.
Bane in Dark Knight Rises could do a couple things
Eat through a straw
A friend of mine broke a his jaw and had to get it wired shut. He received sustenance by consuming liquid food through a straw. Some foods work better than others -- steak just isn't meant to go through a straw -- but it works. He did lose a considerable amount of weight, but that was mostly due to the increased inconvenience of eating, not the lack of achievable nutrition.
Eat through an IV
Aka Parenteral nutrition. This is necessitated by a variety of medical conditions and can sustain a person indefinitely. It bypasses the entire digestive system, not just the mouth, and there are a number of complications. But is it possible.
And there are other ways as well.
Due to the extreme nature and complications of prolonged IV-only nutrition, I'm inclined to believe ingestion through the mouth via a straw. His mask could even be designed to make this easier.