You are not allowed to tap out of a receptacle that does not have a ground. Don't know what jumper you are referring to but hopefully not an illegal bootleg ground jumper. Difficulties in routing new wire don't make exceptions to following code. Perhaps there is an exterior wall nearby which you could take conduit outside the house to the service panel and then feed your new outlet and perhaps others with surface mounted raceway.

Any access from below?

MANY thanks..... you guys/girls have been a source of great advice over the years as I flounder around my house.

the outlet in room b is grounded; house was just sided and any exterior conduit is n/a.

I believe i have access from basement to pull electrical up through wall to room a.

raceway may have to be the way if I can't gain lower access to pull wiring uo into room a.