Was Ethernet ever bidirectional over a single coaxial cable or single twisted-pair line?
The earliest forms of Ethernet were not only bidirectional, all hosts on a network shared a single coaxial cable. This was a defining characteristic of Ethernet and the motivation for the Carrier Sense Multple Access with Collision Detection (CSMA/CD) feature.

According to Wikipedia,


  Original Ethernet's shared coaxial cable (the shared medium) traversed a building or campus to every attached machine. A scheme known as carrier sense multiple access with collision detection (CSMA/CD) governed the way the computers shared the channel.


This scheme was maintained in the 10BASE5 and 10BASE2 physical media implementations, both based on coaxial cable. It was not used for twisted-pair implementations.