Following are D&D 5E rules that can be used to adjudicate attempts to ride rodeo-style bucking animals like one of the Bulls of Crete at the Megalos Ellada farm, one of the places described as part of Skirmisher Publishing’s “In the Footsteps of Hercules” universal sourcebook.

This is the first of four challenges characters can undertake over the course of a festival day at the farm and takes place just after sunrise. It is followed by three others, Herding the Cattle of Geryon, Stealing the Apples of the Hesperides, and Battling the Mares of Diomedes. 

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As described in “In the Footsteps of Hercules,” each of the bulls will be saddled and in stalls that open into the 50-foot-diameter circular stage of the theater at the farm and anyone who decides to ride one will be instructed to position themselves above it. Then, when a rider drops onto the bull, the stall will open and the animal will charge into the performance area and begin buck­ing violently in an attempt to dislodge the person on its back.

For each round someone is on the back of a bucking animal they will suffer a number of hit points of bludgeoning damage equal to the creature’s Strength modifier. Riders will also have to make a Strength (Athletics) or Dexterity (Acrobatics) check to avoid being thrown off, with a DC equal to 8 + the creature’s proficiency bonus + its Strength modifier; characters proficient in Animal Handling have a +2 bonus on this check. Anyone thrown will suffer bludgeoning damage equal to 1d6 + the Strength bonus of the bull, be knocked prone unless they succeed at a DC 20 Dexterity (Acrobatics) ability check, and be subject to attack by the animal if it is so inclined.

So, for example, a character attempting to ride a Bull of Crete that has Strength 19 (+5) would suffer 5 hit points of damage each round they remain on the beast and have to succeed at a DC 15 Strength (Athletics) check to stay mounted (at +2 if they are also proficient in Animal Handling). Anyone thrown from the bull will suffer 1d6+5 hit points of bludgeoning damage and possibly be knocked prone when they hit the ground, and in either case will thereafter be subject to attack by the animal.

Once the bull throws a character it will certainly attack any that are still moving, making a trampling charge in conjunction with a gore and then a possible stomp as a bonus against any that are standing, and a stomp followed by a stomp as a bonus action against any that are prone.

Companions can dash into the ring to assist the rider in any number of ways, to include helping them to their feet as an action (allowing them to stand up as a reaction or bonus action rather than losing movement); casting healing or other magic on them; or carrying or dragging them out of the ring. A friend might also attempt to distract the bull with a DC 15 Wisdom (Handle Animal) skill check, possibly taking the Dodge action to reduce the chance that it will hit them, or jumping into a barrel for refuge. If a bull attacks a barrel with a character in it, the creature will automatically hit but will inflict just 7 (2d4+2) bludgeoning damage rather than what it would normally do with a gore attack.

If the characters appear to have the situation well in hand the staff will not intervene until they have gotten a thrown rider out of the ring, and will then move to wrangle the bull and lead it away. If someone is unconscious or killed, however, the owner Alexander and some of his helpers will begin moving into the ring the round after the rider is thrown, get control of the bull, an extricate anyone who needs assistance. 

Cretan Bull

These beautiful but hulking bulls are descended from those that were bred many centuries earlier by the ancient Minoan royal house of Crete. They can be found and are actively bred at a number of places, most notably the Bullpens of Knossos, located in a palace complex on the island of Crete itself, and at the Megalos Ellada farm on the Peloponnesian Peninsula of mainland Greece.

Cretan Bull

Large beast, unaligned

Armor Class: 12 (natural armor)

Hit Points: 30 (4d10+8)

Speed: 50 ft.

STR             DEX             CON             INT               WIS              CHA

19 (+5)         12 (+1)         14 (+2)         2 (-4)           12 (+1)         9 (-1)

Senses: Passive Perception 11

Languages: —

Challenge: 2 (450 XP)

Trampling Charge. If a Cretan Bull moves at least 20 feet straight toward a creature and then hits it with a gore attack on the same turn, that target must succeed on a DC 15 Strength saving throw or be knocked prone. If the target is prone, the bull can make one stomp attack against it as a bonus action.

ACTIONS

Gore. Melee Weapon Attack: +7 to hit, reach 5 ft., one target. Hit: 15 (3d6+5) piercing damage.

Stomp. Melee Weapon Attack: +7 to hit, reach 5 ft., one prone creature. Hit: 12 (2d6+5) bludgeoning damage.