The longer the time between the shot and field dressing the deer the less time before it starts to bloat and bacterial growth accelerates.
The best is to get it in the shade & field dressed within 15 - 20 minutes if possible. Then  rinse with cold clean water (bottled water works), dry the cavity with paper towels, cover the tenderloins (in left in) with waxed paper or plastic wrap and fill the cavity with bags of ice.  
    Then get it to the butcher or into a cooler or freezer ASAP.
    An analogy that I use is to imagine a T-bone steak, pork chop, or chicken warmed to body temperature then placed outside. How long would you be willing to leave it outside at a given temperature before you would start to worry about eating it? In most cases common sense will dictate the correct answer.

Good luck hunting,

Dave