The data sheet says it has a 71ksi yield, I see no reason to doubt it. Cold drawn is likely stronger near the surface which would be an advantage for bending resistance. SAE 1045 means it means it is carbon steel with 0.45 %carbon. The primary feature or the material you list is a precision dimension surface . It will have low toughness but I can't imagine toughness is needed for a bar bell bar. It is roughly half the 150,000 psi strength you say you want. Addenda; I think the practical source is weight equipment vendors. Looking on the net I find high strength bar is a custom order type product; easy enough to find and heat-treat but in quantity like a ton plus. There is a product named "stress proof " bar that is close , SAE 1144 ,a cold worked free machining steel with about 0.44 % carbon. It may also not be easy to get in a small quantity.