A Niche in Time: “One of the Worst Catastrophes in the World” by Doug Messier at Parabolic Arc on 9/26/17 describes the May 6, 1937 Hindenburg Zeppelin disaster than ended the age of passenger flights on rigid airships. More in a moment on the ticket prices for transatlantic travel.
Several factors led to the end of rigid airships. The disaster took out half of the Zeppelin fleet, the U.S. blocked export of helium so the German company had no choice but to use (and would have continued using) explosive hydrogen, fixed wing aircraft were emerging as an alternative (specifically the then-cutting edge DC-3), Zeppelin travel was more expensive than ocean liners, and the disaster destroyed public confidence in the Zeppelins.
Check out the full article for more details.
According to the article, here are some tidbits on the cost of travel to cross the Atlantic at the time on the luxurious, faster airships and slower cruise ships: