I think what makes the idea "work" and what makes women pick the bear is the mental image of being innawoods. The woman knows that she is not supposed to be innawoods all by herself because, after all, she's a woman.* A bear IS suppose to be innawoods, and it might just walk away from her and not attack.
If there's a man out there all by himself, he's seen as weird, possibly low social status, like a hermit or a hobo or something. Or else he's been stalking her with the intention of raping or killing her. Presumably the woman imagines that she doesn't really know what she's doing in the woods, while it's tacitly assumed that the man does know what he's doing, and knows how to get around. She encounters him because he wants her to encounter him, or he reveals himself to her. Current culture (slasher movies, Texas Chain Saw Massacre, Friday the 13th, etc) has promoted the idea that solitary strange men in the woods are rapists, murderers who can't get laid (Ted Kaczynski is a real-life example) or just plain weird (Christopher Knight). This isn't an unreasonable inference, really, although the idea has been overhyped in popular culture per the above.
They should ask this question again a few years later, in variant versions, to see how women would respond. Groups of people. two men, an all-male group, a male-female couple, and a mixed group. These imply some previously existing social interaction. The solitary man implies none.
*There are a very few exceptional cases. The Russian "Old Believers" include at least one woman who lives in total isolation, and devotes her life to god. This is extremely unusual behavior for a woman. All-female collectives include things like convents and lesbian separatist enclaves (which are, themselves, sometimes situated innawoods). I think there's some Peshmerga Kurdish women who learned to fight and sustain themselves in units in the hills by working together.
