I came across this and though I'd give it a try. I don't really like grapefruit, to eat, so wasn't going to miss this or be concerned about "wasting" a grapefruit (ok, my beautiful Bride does, but she gratefully sacrificed one for me), but I'm always looking for interesting natural ways of cleaning. The original posting is here.
I found this to work out fairly well, certainly the tub had the smell of citrus/grapefruit, at least for a little bit, but there were some spots, especially in the corners, which needed a little elbow grease, ie. working at it with your fingers, to remove the accumulated soap scum. I guess the key here is the combination of salt and citrus. This works not only on the shower/tub, but also on tile, your toilet, sinks, most everything in your bathroom.
1 grapefruit, cut into half
1/4 - 1/2 cup kosher salt
Sprinkle salt liberally on the grapefruit half. Scrub around your tub, squeezing juice over the fixtures before scrubbing. Renew the salt on the grapefruit every few moments (you can put the salt on the "floor" of the tub. Rinse all the pulpy bits away when everything is clean and shiny.