Short Answer: At least 10
If we apply this link, even the smallest motorcycle has 3 Horsepower (HP). That's the equivalent of 2,200lbs (1 Horsepower = 550 lbs moved one foot over one second). Going by the Lifting/Breaking table on pg334, we see that 1HP (~250Kg) falls between a strength of 4-5.Low and behold, a horse in V20DA has a strength of 4! But if that holds true then... Uh oh. That puts the smallest motorcycles at a Strength of 10 by that logic - 1650lbs (~748Kg)
However! Without some very special circumstances, this would not be mechanically possible.
Movement rules say on pg333
Taking another action while moving is possible, but each yard/meter moved subtracts one from the other action’s dice pool. Note that injured characters cannot move at maximum speed. Also note that Celerity modifies the character’s movement speed.
Arguably the mounted combat works because the horse in question is doing the movement and the character is just doing a "weapon strike" or "Great Blow" maneuver at the end of it. Thus you are also taking a Multiple Action penalty on top of the above.
They also don't do the kindness of giving horses a speed, which means I can only rely on the basic Dex (2) x3 +20 meters/turn (appx 3 seconds) in combat, making a horse move 26m at a dash which I think we can all agree is far from realistic. Going by this link, your average horse at full gallop is about 30mph.
Using this link for its nice and neat tables and comparing to the chart on page 259 in the V20 core book, we can assume you can go up to the safe speed without penalty is 70mph with the smallest bike. While this isn't RAW (really no rules for vehicle based anything other than rough conditions for a Ride/Pilot check), I would argue that this means you would get two dice added to damage per turn (70 / 30) for "building speed" per the Mounted combat rules.
Tagging back to the movement penalties, 70mph is about 30mps. Since a combat turn is supposed to represent 3s, that means you would be coming out of the gate with a -90 penalty to your dice pool.
Last but not least, we can also discuss how many hands to have/need to do what you're trying. Without something like Obtenebration 3 or Vicissitude 5 you need at least one arm to "pilot" and another to wield a weapon. Ideally you'll need two hands for the vehicle. I personally see this as where the Multiple Action penalty comes in, but it is a logical consideration before we get to mechanics.
The above is using only rules in V20, but we can also step into another game of the same system - Mage 20.
Falls and Impact > Ramming and Slamming (Mage 20 Core, pg439)
Ramming into, or being rammed by, other characters or solid objects (walls, tables, vehicles, etc.) may – at the Storyteller’s discretion – inflict one die of bashing damage for every 10 feet (or three yards) of velocity at the time of impact. A dude who runs 20 feet before slamming into a wall, for instance, might take two dice of bashing damage from the impact.
If that object’s Durability Trait is higher than the character’s Stamina Trait, he may take an extra automatic bashing health level from the impact. A car that had traveled 40 feet within the previous turn, for example, would inflict four dice of bashing damage for its velocity, plus one health level of automatic impact damage to whatever it hits because… well, it’s a car. If that impact exceeds both the object’s Durability and its Structure, however,
then that object could be destroyed, at the Storyteller’s option.
Objects or characters that smash into each other at roughly
equal velocity take the total of both impact dice pools, plus one
additional automatic success for each turn they were traveling before
they hit, to reflect the cubed effects of colliding velocity and mass.
A flying object loses one die of effect after the first 20
feet unless it’s self-propelled or aerodynamic, two dice after
30 feet, and three after 50 feet. A thrown table, for example,
loses momentum thanks to its mass; a motor-powered car,
however, does not.
Armor, because it’s designed to protect against impact, reduces ramming and slamming impact by the usual amounts. These impact rules do not affect weapons, as impact damage is already figured into the weapon’s normal effects.
And Vehicle Systems > Ramming and Collisions (Mage 20 Core pg459)
In order to avoid absurdly complicated rules, assume that a vehicle ramming a character inflicts that vehicle’s Durability in bashing damage, plus one die for every 10 MPH (14” per turn) that the vehicle was traveling at the time. Thus, a crotch-rocket motorcycle ramming someone at 50 MPH inflicts eight dice of bashing damage, but a limo going at that speed inflicts 10. Certain vehicles inflict additional dice of damage simply
because they’re bigger and harder than a character is. The limo in question actually inflicts 13 dice of damage because it hurts to get rammed by a limo. (For additional levels of damage, see the charts below.)
Passengers inside a colliding vehicle take the usual damage, minus that vehicle’s Durability rating; if they’re strapped in, halve the damage they would normally suffer. In many cases, the Storyteller can simply employ the cinematic trope of having important characters more or less unharmed and unnecessary characters incapacitated or killed in a crash.
With that in mind, it converts the extra die to the pool into an auto success per round building speed, but the rider of the motorcycle is quite likely to hurt themselves in the process. It also still caps the dice pool based on maneuverability, and may still require penalties for not being solely about the attack or the driving alone.
