First of all, if it was truly downtime, I doubt the resident would have any ill feeling. Odds are she wasn't surfing facebook when you asked. She was probably doing important tasks for her patients, and you weren't doing anything to help. If your resident is doing work, and you are standing around, just assign yourself a role. For example, I'm going to fill out this urology consult for Mr. Smith, I'm going to go check labs for the list, I'm going to look up that chemo protocol for Ms. Jones, etc, etc. I think a lot of people on this thread are overestimating the number of activities which are resident-only. If they are busy, there is probably plenty you can and should be helping with.
That said, some residents do need to do a better job taking care of their med students. It is much appreciated when a resident confirms that you got a chance to eat or gives you a break if there is truly nothing going on.
Remember, this isn't about you you you. This is about patients, then team, then you. You may feel entitled by your tuition dollars, but believe me, the resident who is making minimum wage to work double your hours, and is struggling to pay off that same tuition will have little sympathy for you. Some missed meals and sleep are a part of this.