Can you get bedbugs from a blanket?

Not if it is a new blanket but if it is second hand blanket, it then is distinctly possible some unhatched bedbug eggs will have been laid in crevices from previous user, and these very tiny white spots stuck to a hard surface in the blanket may not be apparent when you first put it on your bed. It is always better to protect your bed from bugs with mattress protector that are available these days.