Bessie was the wife of Hosea Matthews. After their marriage, the two briefly attempted to leave the life of crime behind, but Hosea eventually drifted back into it. Despite this, Bessie still loved Hosea, and the two remained together. She died in an unspecified year prior 1899, after which Hosea was "drunk for a year."
In the mission "Exit Pursued by a Bruised Ego", while in Grizzlies East, Arthur mentions that Hosea was "in this area with Bessie" at one point, when the two were living together. Hosea's familiarity with the area (particularly Moonstone Pond, which he seems to remember) supports this.