All deep/narrow chested dogs are prone to bloat (Danes, Dobies, Weims etc). Being particularly large for your breed or having a nervous disposition also seem to be factors.
However, Bloat absolutely has a genetic component. Many old time Poodle breeders say that Bloat was relatively unknown until about 30 yrs ago. Some people point to the bottle neck of the Wycliffe dogs but that is just speculation. The truth is, you can see Bloat run in lines. Having a parent or sibling who bloated greatly increases an individual's risk of Bloat.
With my own bitch, I have now discovered that three of her siblings have bloated. Clearly genetic.
Bloat used to be an older Poodle disorder. You wouldn't see it until a dog was 9+ yrs old. This can make it difficult to get out of a line because a breeder may have multiple generations on the ground before they realize that they have a problem. Unfortunately we are now seeing bloat in Poodles as young as 4 yrs old.