The problem with this question is that eating would probably not be a problem for Bane.
First, we don't see Bane eat or drink, so we cannot know for sure how he does this. But does it matter? It's for the same reason we don't see anyone going to the bathroom in Star Trek, on almost any movie or series, it's irrelevant to the story or the development of the character.
Second, as I stated in the minute following the submission of this question, the problem could be easily countered by using a straw. I made this with an allusion to Mass Effect's Tali. She is a Quarian, an alien species confined to an enviro-suits because of their weak immune systems. She used this method to get drunk without having to remove her helmet. We know that because they made a joke out of it, but it's otherwise irrelevant.
Does Bane use a straw to eat? Maybe, that one of the many method he could use. But who knows, he could chew Buuble Gum under his masks and we would not know!
