Finally a clarification has been made: it's a bicycle!
The original post above assumes motorbike because why would anyone charge at anyone with a bicycle?
But let's re-answer with the clarification
In order to understand why, you need to see why horses were chosen in the first place: because they're fast and menacing. The point of a charge is to deter the enemy with a thundering shock and break the enemy ranks, this is impossible with bicycles because:
1) Cycling a bicycle requires physical effort on the rider, by the time they've reached the enemy while maintaining a charging speed, they'd be exhausted, which is not a goal of riding something in the first place.
2) If you crash against anything while cycling, you'll most definitely fall and not be able to continue your charge, the pointy end might hurt any poor sod that got stuck on it, but it also will render the bicycle useless until the guy is taken off the bike.
3) The momentum a bicycle provides is much less than that of even a young horse, thanks to the fact that bicycles have much less mass and weight, most people can carry a mountain bicycle, virtually nobody can piggyback a foal.
4) It is possible to have a bicycle with one cyclist and one archer to cycle-by, this is true, similar to a chariot archer, but a chariot archer has the luxury of standing on a relatively stable platform, which the passenger of a bicycle doesn't have. The closest you can get is if you utilize a bicycle with support wheels, which technically would make it a quadcycle. A Tricycle would also work well.
An archer would actually prefer staying behind the enemy lines and not join the frontlines. The "arc" in archer refers to the shape an arrow makes as it flies to the heavens and fall down to kiss gravity, this allows archers to shoot from great distance, the most popular long-distance archers being English Longbowmen. When archers join the frontlines they're usually as Chariot Archers that have fast mobility and don't need to fear enemy infantry (and relatively safe against cavalry too), or they're horse archers, which are archers themselves riding a horse, both of which are there to do ride-bys.
There is not much point in having archers charge at the enemy.
At most, bicycles will help you traverse the landscape, and not much beyond that
Original post for motorbike:
Unlike bikes, Horses are capable of standing upright with no support, largely thanks to the fact that they have 4 feet instead of 2 wheels. This allows you to take your hands off the reins for a moment and do something else like fighting while being stationary.
Even if we assume that your bikes are American bikes the likes of Harley Davidson instead of Japanese bikes the likes of Kawasaki (the ones used in MotoGP) or even worse an Italian scooter, charging at something with a pointy tip at the front might cause the rider to fall down along with the bike, and as anyone with a huge bike can tell you, getting it back up is a pain, even more so during a skirmish. To test this theory, try to charge at a fridge cardboard box filled to the brim with enough weight to simulate human weight, see if you can withstand it and not fall down.
Then there are other issues:
Horses are tall, we're not talking ponies here but real horses, this means if someone slashes at you, they'll get to your feet first before your head, the same cannot be said to bikes. This trait is obsolete with the advent of guns, but if you need to charge at the enemies for melee fight in the first place while the enemies have guns, you probably should replace your commander instead of your ride.
You also need stability to ride a bike, something that will interfere with your ability to swing weaponry. If you charge with a lance, the drag from piercing someone's chest might cause you to lose a bit of balance. Not a problem for the best of the best, I'm sure but that's something to think about.
Finally, bikes are the worst against offroad like the woods or rivers. They're cumbersome to turn around and if you get stuck on a mud, Kratos help you. Not to mention the complex nature of such machinery, so many things can go wrong.
It's not all doom and gloom, bikes are very good on plains and they don't need horse riding training like horses, you also can build bikes faster than you can raise horses, and they don't poop, so there's the morale boost.