Is it common for a child with autism to not want to ride a bike?

Oh yes: Children with autism have very definitive ideas of what normal is for them. They are often risk adverse and do not want to feel out of control. Riding a bike is a risk for them, and makes them feel out of their comfort zone. Some may take to it, but many would not. Especially while learning to ride. Some may object to the sensory nature of wind in their face or the inherent lack of balance.

Anything new will be: Rejected at first. Kids with autism do not retain complex, novel information quickly & require repetition of the movement. Remember, verbal instructions may not work & he has difficulty mimicking your motor movements, like he did with pat-a-cake & peek-a-boo.Pictorial cues, books about riding a bike & possibly phyical therapy to teach him how to ride a stationary bike may have to happen first.

Absolutely!: Autistic children have high degree of need for sameness and anything new will need to be introduced more piecemeal than what you would usually think. Also children with autism may have motor balance and coordination difficulties. That is why therapies such as occupational, speech, and physical are part of the ball game based on the unique personal needs. Take care.