Bergen St and Bedford Ave, 1950s.

Bed-Stuy (Bedford-Stuyvesant) was as the name implies, the area bounded by Bedford Avenue on the west, Stuyvesant Avenue on the east, Fulton Street on the south, and bounded by Broadway on the north.

It became slightly less rigid, and the eastern border extended in some parts to what is now Boyland.

If you check the late 60s and early 70s, part of the area claiming to be Bed-Stuy was Ocean-Hill Brownsville.
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Bergen Street and Bedford Avenue was definitely not Bed-Stuy.

I.M. Pei likewise believed that Prospect Place between Kingston and Albany was Bed-Stuy in 1968:

http://www.pcf-p.com/a/p/6611/s.html

'Bed-Stuy' is/was probably more of a metonym for 'Black Brooklyn' than an actual piece of land, as Harlem is/was in Manhattan.

Yes, I.M. Pei would say something like this, being a voice of the wealthy in the 60s.
I remember reading an article in the NYTimes magazine section. It spoke of a crime being perpetrated, and identified the perpetrator, who lived on Ocean Avenue along Prospect Park, as coming from the Bedford-Stuyvesant section of Brooklyn

This just goes to the meme that "history" is HIS STORY.

The people who lived there are continually ignored when they describe who and what they are.

fyi
A metonym
is a figure of speech used in rhetoric in which a thing or concept is
not called by its own name, but by the name of something intimately
associated with that thing or concept. For instance, "Westminster", a
borough of London in the United Kingdom, could be used as a metonym for
its government.