Do bicycle riders have the same rights and responsibilities as automobile drivers?

They vary from state to state in the USA, so it would be best to lookup and read the laws of the state you plan on riding in.
signal your turn prior to crossing through the bike lane at the dashed striping signal your turn prior to crossing through the bike lane at the dashed striping ------------------------------------------------------------------------------------------------------------ they have the same rights and duties as motor vehicle drivers (within certain expectations).
they have the same rights.
They can usually ride anywhere the person riding would like to drive or go

the same rights and duties as a driver of a motor vehicles