Could a full bladder be a reason for heartburn?

Unlikely. Bladder is down in the pelvis and heartburn is due to reflux of stomach acid into the esophagus.
Probably not. Your bladder would have to be excessively full for it to cause enough pressure on you stomach to cause heartburn.
Very unlikely. The anatomical location of the bladder is relatively far away from your esophagus. Please see your doctor to get treated for heartburn.