basmati?

Almost back to regular posting, but I came across something that I had to ask the readers here about.

There is a type of long grain rice called "basmati". All the etymologies I have seen say that basmati in Hindi means "fragrant". I immediately had an association with the Hebrew words bosem בוסם - "perfume", and besamim בשמים - "spices". (I wrote about those two words previously here.)

Now I know that the Hindi language was influenced by Muslim rule in India, and many Arabic and Persian words entered the language. However, I cannot find any source that says that basmati was one of those words. It does seem like more than just a coincidence.

Can anyone prove - or disprove - my conjecture?