Just to be clear, I wasn't recommending OXO. They are expensive although they seem good quality. My point was that a suction cup type of mount may work for you. We had some cheapo baskets that were mounted this way in our old shower and they never came loose.
Mike, Sue, Sissy and Little Man
2015 Ford F350 Lariat FX4 6.7 CC DRW
2015 Eagle Premier 351RSTS