Here are some ideas
the key is to use a stiff wire brush on the rust
TRy straight vinegar & some baking soda any other chemicals will harm birds so will the rust itself..... high traces of iron (oxidized or un-oxidized) can actually cause more serious problems than you may think. Ingesting a high amount of iron can cause something called "Iron Storage Disease." This disease will effect the lungs, liver, heart, and continue until the bird is dead. What's happening is that the iron is trying to be held in the liver, but there is too much being absorbed at once so the body tries to compensate and deposit it in other organs. This is a slow infecting process, but it will kill the bird over time. Cleaning the water does not always mean the water is healthier for consumption.
If you use it gently, a wire brush or sand paper may work to help remove that rust.
Try mr clean magic erase or comet