At the very last we know that people were saying "on Bleecker Street" in 1964 because that's the year that Simon & Garfunkel released their song "Bleecker Street," which contains these relevant lyrics:
Voices leaking from a sad café/Smiling faces try to understand/I saw a shadow touch a shadow's hand/On Bleecker Street
A poet reads his crooked rhyme/Holy, holy is his sacrament/Thirty dollars pays your rent/On Bleecker Street
I heard a church bell softly chime/In a melody sustainin'/It's a long way to Canaan/On Bleecker Street
Early Google Books matches for 'on Bleecker Street'
The first occurrences of "on Bleecker Street" in Google Books search results are considerably older than Simon and Garfunkel. From Supreme Court [of New York], The East New York & Jamaica Railroad Company against James H. Elmore (1874):
The following is a description of the mortgaged premises, herein-before mentioned: all that certain lot, piece or parcel of land, with the buildings thereon, situate, lying and being in the Ninth Ward of the City of New York, and bounded as follows, to wit: northerly in front, by Bank street, easterly, by Bleecker Street; westerly, by Hudson street; and southerly, in the rear, by the thereinafter described premises, containing in breadth in front, on Bank street aforesaid, eighty-seven feet ten inches, and in depth on Bleecker street, thirty-nine feet, on Hudson street, thirty-nine feet five inches, and about one hundred feet more or less in the rear.
And again in evidence entered into the record by the defendant's attorney, Frank Johnson, in Supreme Court [of New York], Aubelio Quarto against William Newman and John Newman (1905):
I know the Mills Hotel down on Bleecker Street. I know there is a high building there. I remember there being an organ grinder on the street there about the time of this accident, but he was far down, not the place where I was.He was not on the same side of the street that I was on. ... I was on the opposite side of the street from the side that the hotel is on. I went across the street to buy a package of tobacco. I was on the sidewalk at Sullivan Street and I was crossing the street in order to go to the other sidewalk where the hotel is—buy this tobacco. I was going to buy the tobacco near the hotrl in a tobacco shop there on Bleecker Street.
And again—finally in a piece of literature—from The Bradys' Bleecker Street Mystery; Or, The House with a Hundred Doors (1907), "by a New York detective":
Both man and child looked so out of place here on Bleecker street that the attention of the detectives was attracted at once.
"Governor, that's a singular outfit," remarked Young King Brady. "Can that be a kidnapped child?"
Early Google Books matches for 'in Bleecker Street'
Examples of "in Bleecker Street," however, are even older. The earliest Google Books match is from "State of Religion in New York," in The Missionary Herald (May 1825):
...a peculiar blessing has been granted to the Orange-street church, which is about to change its location and occupy a new edifice for worship in Canal-street. The Spring street church, who are soon to enter into their new place of worship in Laight-street, has also partaken in the blessing. The colored Presbyterian Church is in an interesting state in respect to its spiritual interests; and a large blessing has been poured forth upon the Centre Presbyterian Church in Broome-street, and the Church in Brookline. A new Church has been formed in Bleecker-street under interesting auspices.
And from Margaret Askew, "The Conspiracy Acknowledged and Defended: In a Letter to the Rev. William W. Phillips, D.D." (1832):
He wished that I would not mention to any of the others, that I had seen him. I went to Bernard's house, but found his wife only within. In returning to my own house, I met Bernard and Margaret, and in a house in Bleecker-street, they signed the paper, and I administered the oath to them. ...
There are in this extract, two or three little points, in addition to those for which I made it—why did you appoint to meet my husband in the front of your house?—why did you slink around the corner with us, into Green-street, and why did you go into "a house" in Bleecker-street, to obtain the signatures, and administer the oaths?—why were not all these transactions conducted in your house?
And much later, from Junius Browne, The Great Metropolis: A Mirror of New York (1869):
"I lodge in Bleecker street" is a biography in brief. If he who says it be poor, the reason is apparent. If he be prosperous, his morality is questioned at once. And yet Bleecker street is respectable enough, if one have no insight into character and conditions.
All told, Google Books finds at least two dozen unique matches for "in Bleecker Street" from the period 1825–1873—before it turns up its earliest match for "on Bleecker Street." Eventually, however, "on Bleecker Street" takes over. An Ngram chart measuring the frequency of occurrence of "in Bleecker Street" (red line) versus the frequency of occurrence of "on Bleecker Street" (blue line) shows a general trend downward for "in Bleecker Street" since about 1920, and a general trend upward for "on Bleecker Street" since about 1908:
The two frequency lines cross a few times between 1919 and 1947, but today the runaway winner is "on Bleecker Street." If I had to provide an approximate date in response to the question "At what point did more people say (or rather write) "on Bleecker Street" than "in Bleecker Street," I would say sometime in the late 1930s—but it seems quite likely that the change in written usage had to catch up with a somewhat earlier change in spoken usage.