I had one in my kitchen sink. When my sister-in-law saw it, she suggested that I put the sink stopper in, pour 3-4 cups of Chlorox in it (enough to cover the bottom), add a couple inches of water and let it sit over night.
It worked. The sink was sparkling white when I drained it out the next morning. I've done the same thing every few months when I notice it getting stains in it. Chlorox definitely pulls the stains cleanser doesn't.
If you don't want to pour a whole container of Chlorox in your tub, possibly soaking an old rag in it and put the rag dripping wet (do not wring it out) on your stain and leaving it overnight might work.