There will be times when you may have to exert a bit more care and effort to get the job done. If there is a bit of wind, and the distance between fire and exposure is small, you will face a greater challenge. Always remember that the primary concern in these cases is firefighter safety. We would not like to tell a widow that her husband died saving a pile of garbage bags. It just does not make sense to endanger people for property.
Many times we have supervised operations at industrial dumpsters. After ascertaining that hazardous materials were not involved, we usually order an open-butt supply hose line to be stretched. The dumpster was then flooded.
The object is to extinguish the fire in the safest manner possible. It is not your fault that there is a fire. Your just is to extinguish it with a minimum of effort and danger. The removal of a damp dumpster is the vendors concern.