Not to insult your intelligence, but be humble. Some corporate flight departments, or people within them, may be "intimidated" (for lack of a better term) by ex-mil pilots. A "these little jets look like fun" attitude won't work. Express your desire to learn a whole new side of aviation through corporate flight ops.
As an ex-mil (now corporate) guy myself, I can say I have learned a ton.
Work your contacts and expand your network. Good luck.