Wow, so many conflicting answers. Here's a fourth. I grew up in the northeast USA and to me, dry bread means stale bread or possibly bread which was never very good in the first place. I've never heard of any of these other meanings. To me, "dry bread" contrasts with "fresh bread" or possibly "moist bread."
I agree with Criculann. I'm a native English speaker and this sentence confused me for a little while. I think you could also say "plain bread" here, meaning without any butter, cheese, vinegar, soup, etc. etc. etc. But "dry bread" is not a something you would ever see on a menu, for instance. (Neither is "wet bread!") I wouldn't worry about it too much. :)