Presidents pick *all* ambassadors, with the help of their staff, especially the Secretary of State. They may pick career foreign service types, but can nominate anyone they choose. Ford (or Nixon, I'm not sure) chose Shirley Temple Black, who reportedly did a great job in Ghana and was later appointed by Bush I as ambassador to Czechoslovakia Clinton chose that one, she was his responsibility, regardless of her status before she was appointed.
Well, yes. But some appointments are overtly political and others go to professional diplomates. I don't think there is any evidence that Clinton chose Bodine, rather than ratified a State Dept. recommendation.