The problem with this question is that eating would probably not a problem for Bane. But, after 2 month it gathered more than 10, 000 views, so I think it deserve to be stated in an answer.
First, we don't see Bane eat or drink, so we cannot know for sure how he does this. But does it mater? 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 theirs weak immune system. 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 how knows, he could chew Buuble Gum under his masks and we would not know!