she is very driven and headstrong but also pretty sensitive, and generally not good at expressing that side. she absolutely hated cate's ex-husband, was a huge champion of them breaking up, and was pretty devastated when he showed back up like he did. so i think by default of not being a dick busy would've liked sawyer. as much as they love each other, cate and busy also have a tendency to butt heads a lot, frequently. so i think it's likely she would have tried to maintain a friendship with him.