Bhati most likely lived during Mufasa's reign. She met and befriended Nala when the latter was a cub and presumably met Simba through her.
During early production of the film, Bhati was intended to be a childhood friend of Simba and Nala's. Beyond this, her role in the film is somewhat obscured, though it can be safely said that she was an active participant in Simba's impulsive antics and loved being around her friends, as indicated by her numerous concepts.
In most sketches, Bhati is drawn to be long-bodied and slim with skinny legs and a long, pluming tail. Her fur is usually depicted as being sandy-yellow, though several concepts display her with brown, orange, or red fur. Her ear tips, eyebrows, legs, and tail tip are always darker than her main pelt while her chest is lighter. In newer concepts, she is given freckles and amber eyes.
Personality and traits
Not much is known about Bhati's personality. However, according to Mouse Under Glass, she is a "wisecracking" friend of Simba and Nala's. It can be assumed that she was better friends with Nala than Simba, as she was a member of Nala's gang rather than Simba's, which at the time consisted of only Timon and Harold.
The Lion King Wiki has a collection of images and media related to Bhati.