Is there a difference between how long fresh herbs and vegetables last if they are in a plastic bag or in the open?  If it does, is there a break-down of which ones it does make a difference for - example: cilantro seems to get mushy very quickly in a bag but last for a week in the open, but scallions last much longer in a plastic bag and deflate almost immediately in the open. 
It depends on the moisture content. If the vegetables are wet when put in they will get mildew and go soft faster because the water has no place to evaporate. This is made worse when leafy greens are put in bags since they have so many nooks and crannies to hold water, and they seep out their own moisture content because of the large surface area. Try drying off the veggies first or putting them through a salad spinner to get as much water out of them as possible. 