**Neither a teacher nor a native speaker.**
The correct word is bicycle.
I don't think the 2nd sentence is correct English anyway.
You can say:
He can ride a bicycle.
He can ride bicycles.
He can ride bicycle. - I will be very surprised if this sentence is correct...
By the way, the word bicycle can be used as a verb too.
So you could also say:
He can bicycle.
However, I'm not sure if people actually use it this way.
Student or Learner