Click the bone compensation button. When enabled the child bones are automatically manipulated so they appear not to change. Note you'll have to key the child bones.

@infrid, just wanted to clarify. Terminology can be annoying sometimes, just ask Nate he often has no clue what I am talking about Anyways, there are two ways to resize your bones, one is by changing the length (which is merely a visual guide until we implement snapping) and the other is scaling.
Like Nate said you can use bone compensation, just make sure you hit K afterwards to key all changes since your child bones will scale the opposite of their parent.
Another way that I've used myself in some cases (despite slight overhead) is to parent a zero length bone to the bone you want to scale and place your image on that instead, then scale the zero length bone instead. You still do translation and rotation on the original bone. This way you can do scaling without affecting the child bones, since it won't have any children. Just keep in mind, this adds a little overhead. We are implementing a way to disable scaling and rotation inheritance as well.