I'm not like a Quiet fan or anything -- I've aired my grievances about her before -- but I can buy her falling in love with Venom, or at least developing strong feelings for him.
The following is the way I interpreted their bond.
She tries to kill him, not once but twice (at the hospital and the ruins). Despite this, Venom spares her twice (at the ruins and MB). He also rescues her at the end.
Not only that, but he trusts her enough to accompany him on missions. When your enemy not only spares you but also forgives you and goes the extra step of trusting you, that says a lot about their strength of character and makes an impression.
But it also seems implied they share an intuitive link. It doesn't matter that she doesn't speak; Venom just understands her regardless. Not enough to know the details of her life or the particulars of her secrets, but he seems to have a good emotional read on her.
Venom treats her like a human being -- not the monster she is -- and understands her in a way she hasn't felt understood before. Maybe they can relate because they're both "living weapons," and over the course of the story he softens her through selfless acts and the way he cares for the MB family.
And like Ocelot says during the torture scene (something BB allowed for the sake of stability, and something Quiet seemed to understand, not begrudging him for it): "She's in love with the legend." So maybe the mythical quality of "Big Boss" captured her imagination, as well. She can see why others hold him in high esteem because she sees his heroism on the battlefield.
Just some thoughts on why she might've developed feelings for him. It could be purely non-romantic, but whatever it is, it's there.