To get rid of the Brown colored rust at the bottom of a porcelain toilet bowl (or even on a shower floor) due to hard water, you'll want to get some Loctite Naval Jelly Rust Dissolver. The pink Naval Jelly works wonders to clean up brown rust stains in toilet bowls, in showers, or to clean up rust around faucets.
To clean the rust out of the bottom of the toilet bowl, simple shut the water off at the toilet bowl, flush the toilet and let the water drain out (you can scoop out all the water from the toilet bowl, but it's not necessary). Now "dump" or put a little bit of Naval Jelly in the toilet bowl. You can let it sit for a bit or you can start scrubbing it with a toilet bowl brush (or use an old tooth brush, or scrub pad). I actually think a tooth brush works well, since it's small and easy to scrub the rust off. If all the rust doesn't come off at first, just put some more Naval Jelly in the toilet bowl and let it sit for a bit, and then brush it again until the brown rust stain is removed and your toilet bowl looks brand new again!