"Genuine leather" is the first phrase that popped into my mind, "real leather" is the second.

"Genuine leather" is the phrase a manufacturer would be likely to use. If you wanted to buy one online, "genuine leather" would be the phrase to search for. "Genuine" is the opposite of "fake," and "fake" suggests cheating or deceiving. "Genuine leather" means "we're not trying to fool you, it's leather."

"Real leather" is what people would say in conversation. "Oooh, what an elegant handbag. Is that real leather?" The opposite of "real" is "imitation" (or "artificial" or "synthetic" or "man-made.") 

"True leather bag" is just puzzling. A native speaker wouldn't be quite sure what it means.

"Original leather bag" would be very confusing, almost misleading. In the case of fashion, "original" usually is used in connection with design, not material. It means that something is the actual product of a famous designer, as opposed to a "copy," an "imitation," a "knock-off" or, increasingly nowadays, a counterfeit. 

"Of course this is a knock-off, there is no way I could afford an original Karl Lagerfeld."

“Real leather” and “genuine leather” are both correct.

The more general term is “real leather”. Genuine leather is a type of leather that’s real but not high quality. See here: <a href="https://www.businessinsider.com/leather-buying-guide-2014-12" style="-webkit-text-size-adjust: 100%; -webkit-tap-highlight-color: transparent;">https://www.businessinsider.com/leather-buying-guide-2014-12</a>;