Here's the sub-heading from the article you linked to:
"The story: Robert Moses ordered engineers to build the Southern State Parkway’s bridges extra-low, to prevent poor people in buses from using the highway. The truth? It’s a little more complex"
No evidence besides the direct testimony of a person that worked on the project given to one of the best biographers in a piece of work that won a Pulitzer Prize. Also, the physical evidence of the bridges. Circumstantially, the man was openly racist, and openly used design to segregate.
The assertion isn’t that you couldn’t take a bus to the beach. The assertion is that you couldn’t take a bus from the inner city neighborhoods to Jones Beach, which was true.
https://www.bloomberg.com/news/articles/2017-07-09/robert-mo...