If you go on the Internet and type in the name Tarbush on Google, quite a bit of info comes up.
1. It appears that the name is middle eastern.
2. However, I know that it also has occasionally appeared as a variation of Terbush, which is German-Dutch in origin.
I suggest you check it out.It lists a number of Tarbushes in the U.S., mostly in the southeastern part of the country, but also a few in Ohio.
None in New York state, which makes one think they may not be connected with the Terbush name, but that isn't certain as there are also no Torbushes in New York state, but the Torbushes in North Carolina and Georgia seem to have descended from the Terbushes of New York.