Firefighters were called to the scene in the 100 block of Long Yard Lane about 5 p.m. on Tuesday.
The flames erupted in a 2nd floor bedroom where the girl's body was found. She was reportedly playing with a 5 year old cousin who escaped the inferno.
The grandparents told the Wilmington News Journal they tried in vain to get upstairs to rescue Bethany, but were driven back by the smoke and heat.
Damage to the home has been set at $75,000.
Information from: The (Wilmington, Del.) News Journal, http://www.delawareonline.com