Betsy the Brahmin appears to be a standard water brahmin associated with the cut character Kevin Hargrove. Although she is not placed anywhere in the game, a number of resources placed in the game indicate she was somehow tied to Freeside's north gate, in particular a disabled animal pen and gate internally referenced with her name.
There are also indicators that Betsy would have served as some manner of companion, likely temporarily. An additional quest titled VDialogueBetsy (FormID 0015435e) contains two partially complete dialogue options: "Betsy, I need to go on by myself. Are you going to be okay, girl?", and "C'mon, girl. Let's get going." Both options are incomplete and lack any form of reply or script associated with it.