Yes to both. "Bear" as a verb means to support or carry the burden, or to exert pressure.
"They bear the travel costs" means that they are responsible for the payment of all the costs of the journey.
In the case of women and pregnancy, there are two uses for "bear"....
Women are the child-bearers, that is, they are the ones that give birth. They bear children.
Also, to be a bit more graphic, when a woman is actually giving birth, the doctor might tell her to "bear down," which means to push.