If your city's drinking water contains metals (hard water), it leaves rust stains in the bathtub and bathroom sink: even when rubbing with strong cleaning products, the orange stains do not disappear.
What's the solution? The hydrogen peroxide at 3%, the same as you sometimes use to cure small cuts and injuries. This is a powerful cleanser too. Peroxide is sold in pharmacies, grocery stores and Dollarama, so it's not an expensive product. Stock it, the peroxide can help you with other housework.
Use a spray bottle (also sold at Dollarama!), Pour in the peroxide and spray all rust-stained surfaces, let it rest for at least 10 minutes and rinse!
If you do not have a spray bottle, pour it on a towel and place it on the stains in the bathtub: you will use more peroxide, but as it costs about $1 a bottle, it does not matter! And it will work as well. The important thing is to cover the orange spots with peroxide and wait.
Once your bathtub and sinks are clean, use the peroxide every time you wash the bathroom: you will kill the rust before it expands!