I understand that freshmen at Williams will either be in a single or double room and that 4-6 students share a bathroom. Are the dorm bathrooms more like a locker room where multiple people use it at the same time or are they smaller with only one person using at time?
Picture two toilet stalls, two sinks, and a shower stall. Depending on how you time it, you could be there alone or others could be in the bathroom getting ready for class at the same time. Due to the stalls, there is privacy.
What we were shown on our tour were suites. There were 2 bedrooms with a common room in each suite. There was a bathroom complex in between two of these small suites with direct entry from either suite. The bathroom included 2 sinks, 2 showers, and 2 toilets with each having its owm stall. There was privacy in the toilets, limited privacy in the showers (curtain and recessed entry area), and no privacy at the sinks.
We were told that each bedroom would have 1 or 2 students, so we were left to believe that each of the small suites could have 2-4 students, meaning that 4-8 students could be sharing the bathroom complex.
We were also told that the suites could be either single sex or co-ed.
Our impression was that the set up was inadequate. The idea that as many as 6-8 young women could be sharing just 2 sinks with all trying to get out at similar times in the morning seemed like a recipe for disaster. The idea that this arrangement might be co-ed was too much for us to contemplate.
I must add that I’ve seen worse.
I’ve had a DD and DS go through the same freshman quad set up Bill Marsh describes (with one in Sage and one in Williams) and neither had any problems, nor any timing issues. When we would visit with other parents, even then no one waited for the bathrooms. The bathrooms are more than adequate. This is because no one has the same class or activity schedule. Classes alternate days. Some are MWF, others TT, and others for a loooong single class a week often at night. They start at different times. Some classes start early or mid morning. Some midday. Others start in the afternoon. I know clever students who figure out a schedule that only occurs in the afternoon. 
Some students like to shower in the morning. Some like to shower before bed. Some do it immediately after athletic practice in the late afternoons. Again, no one is on the same schedule. Hence no issues with the bathrooms.
Fear not. Your freshman will maintain proper hygiene, as long as they choose to.
Both my DD and I (and I’m her mom) experienced co-ed dorm bathrooms in our time in college and no one cares. Truly, no one cares. I’m guessing if your daughter requests a single sex set-up including floor and bathroom, she will most likely be accommodated. But at some point in her college career, she will use genderless bathrooms. Consider it all part of growing up and learning to live in community with others. Good luck and please let your daughter know I hope she enjoys Williams! It’s a remarkable place with extraordinary people.
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I appreciate the responses.