First of all, Bessarabia is "is a historical term for the geographic entity in Eastern Europe bounded by the Dniester River on the East and the Prut River on the West," and is now referred to as Moldovia. Like most of Eastern Europe, pogroms, the Holocaust, and emigration significantly reduced the Bessarabian Jewish population.
One significant emigree was German Goldenshteyn (A"h, 6/9/2006), who "arrived with nearly a thousand klezmer tunes (many previously unknown) that he had transcribed over the years." This legacy, now published in the three volume series "German Goldenshteyn: 'Shpilt Klezmorimlach, Klingen zoln di Gesalach,'" forms the basis for the Bessarabian Klezmer repertoire in the US. Goldenshteyn has one available album, published posthumously and available through CDBaby. Klezmershack has a wonderful 1999 interview.
Bessarabian Klezmer, itself, is a border music strongly associated with Balkan and Roma (gypsy) music, and you hear that influence clearly in the quick rhythm and horn bass line in Goldenshteyn's "Medley of Moldavian ... (MySpace clip)". While I couldn't find any video of Goldenshteyn, there is no shortage of musicians who play in the Bessarabian style. Here are a couple examples:
The first is Alicia Svigals, Iliya Magalnyk and Marilyn Lerner playing at The Stone, New York, April 27, 2007. (Recorded by Misha.)
Bessarabian Medley (Klezmer)
The second is the Lansdorp String Trio. I was amazed to see the "violin with a horn (trumpet- violin or Stroh Viol."
"It's an early 20th century invention of John Matthias Augustus Stroh. These violins were made between 1904-42, and during the era of the Bessarabian klezmorim (the 1920's and 30's) widely used by dance band leaders. In modern folk music they may still be found in the Rumanian Bihor district."I can't embed this one, so go see the Lansdorp String Trio video on YouTube. They also have a recording, "Bessarabian Groove" available through CDBaby.