The Bull

The bull is positioned prominantly. It stands stoicly and has turned his gaze to stare at us, staring at it. Interestingly, the only figure that does stare out from the painting.

It's eyes are not bovine, they're human. Lending credence to the fact that this figure has more than one meaning. 

The bull is depicted here out of the normal contexts that bulls invariably appear in Picasso's works. They're either in a bull fight, or they're standing menancing or they're joined with a human head as a minotaur performing all manner of violent acts. There is no doubt that Picasso views the bull as a symbol of violence and power.

But here, the bull is passive. There is even the slight impression of vulnerability about it. It's horns are prominent, but not large nor threatening as the deadly weapons that they are. It screams as it stares back at us. I think this figure is symbolic of several things:

Nationalist Violence

The bull may be the counterpart to the horse (which also has several similar symbolism) representing the victims, the Republicans. 

Male Aggression

Picasso chose to depict the bull testicles prominantly. There is every possiblilty that this symbolises male agression fueled by the testosterone that is dependent on the testies. The bigger the testicles, the greater the testosterone, the greater the aggression. And it's aggression that has precipitated the awful attack on Guernica.

Picasso

The human eyes that stare back at us with the scream suggest that the bull not only has a human function but that this is Picasso himself. Picasso, having read the distressing report of the attack is bringing the nuances and the true essence to us through this painting, through his character representation in the scene.