ukchris welcome to the forum.
It is essential for Clinton to go with a safe, white, Protestant, moderate male, who will be acceptable to women and non threatening to men, someone seen as capable, someone politically experienced, someone she would be comfortable with on the ticket and should she become President someone she would be comfortable working with in her administration.
She goes with Senator Evan Bayh of Indiana, who is also a former Governor of Indiana. The fact he is a sitting Senator from a state with a Republican Governor does not come into play, as Clinton will want his experience, his appeal, and his abilities.
What would happen then if the Republican governor of Indiana loses? Would the lame duck incumbent apppoint a GOP senator to fill Bayh's spot, or would the newly elected Dem governor choose a Dem to fill a Dem seat?