Wikipedia says that the ethnicity is Georgian yet, the two ethnic groups, Armenians and Georgians, have ruled in both Armenia and Georgia. Who was the founder and were they actually originally Georgian or Armenian? I believe it had to have been Armenian but my eyes say it's Georgian.
The Bagrationi dynasty is/was descended from ethnic Armenians, that is true. Unfortunately I don't have the sources on hand with me, but I can give you the means to find them and read more on it (see the end here). However just because the Bagrationi's originally came from Armenia doesn't really make them any less Georgian. They ruled over Georgia for some seven centuries (depending on how you want to count "ruled"), and married local families, so by the end of independent Georgia in 1801/1810, they were thoroughly Georgian. But the short answer to your question is, yes, the Georgian Bagrationi dynasty was founded by an Armenian.
I will admit here though that I am not that well-read on medieval Georgia, which is in part because my focus has been on the twentieth century era, and because honestly there is not a lot of scholars in English who write about (for lack of a better term) pre-annexation Georgia, so any material that is out there is usually rather old (and likely dated), or just not in any serious depth.
Further reading:
Ronald Grigor Suny, The Making of the Georgian Nation (1988, 1994): this is the standard survey text in English of the history of Georgia. It is more focused on the modern (read Russian-dominated) era, but does give some context to the historic eras, and is full of further sources in the bibliography.
Donald Rayfield, Edge of Empires: A History of Georgia (2012): Rayfield's book isn't quite as well-regarded as Suny, but he goes into a lot more detail about medieval and ancient (read pre-Russian annexation) Georgia. If you want a decent overview of the rise of the Bagrationi family, I'd highly suggest this, as he looks into the very question you are asking, and the relationship between the two places.
You may also want to search the works of David Marshall Lang. He is effectively the godfather of modern English study of Georgia, in that he founded the British institute that begat the modern efforts to research the country. I do believe he wrote about that era of Georgia when he was active in the 1960s, though the name of the title escapes me. However his name should show some relevant results.