Is it true that in the US homes every bedroom is designed with a bathroom? In other words, does everyone in an household have an individual / personal bathroom?
No, this is not true. The typical home has a main bedroom for the parents called a master bedroom. These ususally have a connected bathroom, used mainly by the parents/adults. The number of bathrooms typically depends on the number of bedrooms the house has. In a "3 bedroom 3 bath" house, one of these bathrooms will usually not have a tub/shower, and is considered a "half bath(room)" which is designned for guest use. The bathroom that the other members of the house(children) usually share a bathroom.
Average "3 bedroom/3 bath" home:
A) Parents-1 bathroom (toilet, sink, shower/tub)
B) All Children-1 bathroom (toilet, sink, shower/tub)
C) Guest-"1/2 bath" (toilet and sink, no shower/tub)