The staring past Kenzie thing totally fits in with seeing her as a beloved pet. She needed the distraction, so she asked for her story so that she would make noises to distract Bo from her guilt, but still does not care what Kenzie is saying. In short, totally has removed her head even one inch.
And I think I see within the plot what is going on. Canonically we have never been given reason to believe Bo is the sharpest crayon in the box either intellectually or emotionally. They never explicitly compared her to box of rocks, but never done anything that would prevent our making the comparison.
But also her history may explain some of it. Basically she was traumatized by killing her first lover (not explicitly in high school but probably) and then becoming a fugitive. From then on her sex life was exclusively part of being a serial killer and some time rapist. That rules out romance. And as a fugitive the indication (not proven but strongly hinted) is that she did not dare make friends. So social life was casual short term and emotionless. Her last emotional connection was from high school. So basically her social development, her ability to deal with friends and lovers is frozen at the stage of a not very mature high school student. (Probably I'm thinking this through more than the writers, but not necessarily - that last scene with Kenzie may be indicating that they have thought it through. They have actually signaled a few bits of what turns out to be canon fairly subtly in the past, and this is not subtle.)
So when Kenzie proposed being a "sidekick" because Bo was the "toughest" in the first episode, I think Bo translated this emotionally into being in high school and taking someone lower on the social ladder as her BFF. Spending a lot of time around Fae who refer to Kenzie as a pet made this worse, and I think at this point, even though Bo denies it she sees Kenzie as faithful, adorable, sometimes exasperating, but beloved pet.
I think if that is to change Kenzie will have to take the lead. At this point Bo depends on the people she is in a relationship with (of any kind including simple friendship) to define the terms of the relationship more. She may renegotiate at the margins, but overall takes people on the terms they set or leaves them. She is not capable at this of either being the one to define the relationship, or initiate a fundamental change in terms. That is part of the thing with Lauren. Aside from the whole betrayal thing, even if Bo decides to forgive, Bo would have to define fundamental new terms for the relationship, and she is not (at this moment) capable of that.