> This is often very illegal to do on a bicycle.

Most states, in the USA, base their vehicle laws on the uniform vehicle code (UVC). Though they state that those riding bicycles at less than the normal speed of traffic must ride as far right as practicable, they will list a number of exceptions for that requirement. One of those exceptions is if the lane is of substandard width which is defined as a lane that is too narrow for a car and cyclist to travel safely side by side [1]

Since a cyclist is about 2.5 feet wide[3] and many states have a 3 feet distance passing lane, the cyclist, even if they're riding further to the right will still need 2 feet to their right, their width, and 3 feet to their left. That adds up to 7 to 7.5 feet. Given that most surface street lanes are 10 feet wide[2] and passenger vehicle are about 6 feet wide[3], then it's not possible for a car and cyclist to safely travel side by side within the lane.

So the lane positioning you describe when driving a motorcycle also applies to bicycles.

[1] http://iamtraffic.org/wp-content/uploads/2013/01/UVC2000.pdf (section 11-1205 Position on Roadway item 3 -- page 185 of the pdf)

[2] https://nacto.org/publication/urban-street-design-guide/stre...

[3] https://nacto.org/publication/transit-street-design-guide/tr...