There doesn't seem to be any obvious reason people would not admit their actual preferences in the study as presented. What bias would you expect, and why?

You don't think there's any reason for a woman to be embarrassed to admit (even anonymously) what features she finds attractive? Women face extreme scrutiny for their preferences, and they definitely feel that magnifying glass on them. They often don't want to be perceived as setting a high bar. Unless I'm misunderstanding what you're saying - I feel like I'm describing common knowledge.

Maybe? I don't know, ~any of the women I know don't seem shy about their preferences, but I'm sure women I know isn't a particularly representative sample.

I just don't terribly think that masculine or not, neither choice seems socially less/more acceptable to me.

And for my own preferences, even if I was feeling ridiculously overly-socially concious of my choices I don't even know which end of the scale I'd have to pretend to be embarassed about.

It's like the where the guy has two options on the doctors form: heterosexual or homosexual and he writes in "straight"

Feminism finds masculinity/machismo threatening. Any woman that ascribes to being a feminist will say she doesn’t like masculinity so she doesn’t betray her cause, irrespective of how she feels.