Premier Bhavani was a female Barzan in the 24th century and leader of the Barzanian Planetary Republic.
In 2366, when the purportedly stable Barzan wormhole was found not far from Barzan II, Bhavani led the conference that listened to bids for control of it. Because the Barzans were a resource-poor species, the discovery of the wormhole represented a tremendous opportunity for them. Lacking in technical expertise, or experience in handling such matters, the Barzans decided to sell the rights to the wormhole and conducted negotiations with the Caldonians, Chrysalians, Ferengi, and the Federation.
Bhavani oversaw the negotiations and was very close to accepting the Federation's offer when Devinoni Ral, the Chrysalian negotiator, bought out the Caldonians and created an alliance with the Ferengi. Playing on Bhavani's fear of conflict and by creating a false conflict with DaiMon Goss, Ral was able to convince Bhavani to accept the Chrysalian bid instead, even before the results of a mission through the wormhole were known. (TNG: "The Price")
Appendices
Background information
Bhavani was portrayed by Elizabeth Hoffman.
In a 2006 interview, Hoffman recalled the role, explaining, "[..] I had two hours of makeup with tubes and things out of my mouth. And they sent down changes in the script, three or four pages and I couldn’t put on my glasses to work on it. So somebody had to read them out loud to me, and hopefully I could grab on to something." [1](X)
Bhavani, herself, was described in the script as "a strong, no-nonsense, elderly woman; an able judge of people. She wears a breathing device."