Motorbikes were to be featured in the planned level "Roadkill" and were supposed to be used in a similar fashion to the snowmobile from "Cliffhanger". However, along with the level, they were later scrapped.
Concept art for Roadkill.
Call of Duty: Black Ops
In Call of Duty: Black Ops, motorcycles are kept in a warehouse at "Vorkuta" labor camp in Call of Duty: Black Ops and are used by Alex Mason and Viktor Reznov to escape in the end of the breakout. They are an essential part of Mason's and Reznov's plan to escape Vorkuta. Many guards can be seen riding them throughout the escape. The player is given a Model 1887 shotgun to defend themselves while driving while Reznov takes an AK-47. They also appear in level "U.S.D.D.".
Call of Duty: Black Ops II
A motorbike is briefly seen in an opening cutscene to level "Pyrrhic Victory".
Call of Duty: Black Ops Cold War
The motorbike returns in Call of Duty: Black Ops Cold War as the Dirt bike and can be used on Cartel map and in the Fireteam and Outbreak maps.
How to obtain
Bundle Long Road Ahead
Bundle Vehicle Pack: Animal Attack
Bundle Vehicle Pack: Neon Nights
Bundle Demon Dog
Call of Duty: Warzone
The motorbike returns in Call of Duty: Warzone as the Dirt bike. Will be added as part of the Season Four of content for the game.
How to obtain
Apparently the motorbikes belong to Vorkuta's leaders as Reznov states that they are "Within the shrine to the hypocritical decadence of Vorkuta's leaders."