I also have a 9 year old daughter, who visits with her dad every other weekend, and if she is like mine, and there was anything going on other than "sleeping", she will tell you. Kids cant always keep quiet if they are abused, and if you dont see any significant difference in her behavior when she returns home to you, I wouldnt worry so much about it.
She may have her own room with you, but maybe your ex has his own reasons just as you do.
Only if she has a behavioral change, or withdraws from her dad when he picks her up, or you take her to him, she is fine, Im sure.
Bathing with opposite sex is ok, they are too young to even think about anything but taking a bath together. Try not to make it where your daughter is asking questions about everything, it may frighten her, and keep her confused. Im sure she can distinguish between whats right or wrong, she is 9 years old! Most girls are pretty smart when they reach age 7