Was it your grandmother who told you that she didn't have any relatives in this country? Given how large famiies were 2-3 generations ago, that seem a bit odd. Especially since new immigrants often came to live with relatives already here, or the new immigrants' tickets were paid for by relatives here in the US. Who did your grandmother live with when she was a little girl?

Have you traced your grandmother's family back to the old country, via records on Jewishgen? It is possible that the connection between your grandmother and this Bloom family is through forebears who did not come to this country.

I used to think that I did not have any forebears that settled New York City. Except that I had DNA matches whose families only lived in NYC or its suburbs. It turns out that two of my great grandmothers had sisters (who were unknown to me) who came to the US and lived in NYC; it was these sisters' great grandchildren who were the DNA matches to me. 
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Michele Lock

Lak/Lok/Liak/Lock and Kalon/Kolon in Zagare/Joniskis/Gruzdziai, Lithuania
Lak/Lok/Liak/Lock in Plunge/Telsiai in Lithuania
Rabinowitz in Papile, Lithuania and Riga, Latvia
Trisinsky/Trushinsky/Sturisky and Leybman in Dotnuva, Lithuania
Olitsky in Alytus, Suwalki, Poland/Lithuania
Gutman/Goodman in Czestochowa, Poland
Lavine/Lev/Lew in Trenton, New Jersey and Lida/Vilna gub., Belarus