My Mom has been having this problem with her cat too... going in the sink.  Krying is right that the first thing you need to do is rule out a urinary tract infection or other medical condition.  If it is actually a behavioral thing, you can try making that an unattractive area- put down some aluminum foil- they don't like to walk on that and it will make her dislike being right there.  It almost seems to be instinctual for cats to do this- I have no clue why- but I've known several cats that do it, especially if the litter box isn't an option or if it's dirty and unappealing.  Seems like the next best option is generally a drain, which I guess is better than the carpet!  But the best suggestion I can make is to make the litter box as appealing as possible, and the tub as unappealing as possible.  Although you mentioned that the "basin" (I love that you call it that!) is clean and she LIVES in the bathtub.  Why does she live in the bathtub?  That's funny.  I don't know... I almost kind of wonder if there's something about that cool porcelain that they like.  Is she declawed?  Maybe the litter bothers her feet for some reason so she found an alternative that feels better.  I have a cat that is really picky about her litter brand- maybe you could try changing the litter you use.  Just some suggestions!  Good luck! 

If it is something that she just started doing it could be that she is letting you know that she has a urinary tract infection.  If she has been doing this for a long time it could be that she just like whizzing down drains.  Sorry, but my Sammy likes to get in the shower and he aims straight down the drain.  3 litter boxes and he goes out for about 30 minutes a day and still  prefers the drain.  When I catch him before hand I put him in the littter box but next night same thing again.  Use that kitty cleaner in the tub to get rid of the odor or she will keep returning.

Peace

Kat