My Dad came from an Amish family and I have many still-Amish relatives. Whether a given group of them are allowed to use bicycles (or any given technology) is up to the group's council. My relatives in Indiana can use bikes. I've heard the ones around Lancaster County use scooters. Sometimes they can use things they don't own, too.
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Genesis 49:16-17
"Well, well!" said Holmes, impatiently. "A good cyclist does not need a high road. The moor is intersected with paths and the moon is at the full."