When backing out of my driveway I looked both ways and then backed out and a car came around the corner speeding and clipped my bumper. Damage down to other car but not mine. Whos fault is it?

Unless you can prove the other car was violating the posted limit, the onus to ensure the road was clear is completely yours. Even if you CAN prove the other car was speeding, this may not remove all of the fault from you.