In Season 2, Barbara "Bobbi" Morse joins Phil Coulson's S.H.I.E.L.D. team after becoming an undercover agent at H.Y.D.R.A. Both Fitz and Bobbi belong to this team and worked on various missions together. Throughout Season 2, Bobbi seems to care about Fitz and Simmons relationship and how Simmons was treating Fitz after his brain damage. Morse also expressed displeasure when Fitz was followed by Gonzales after stealing the Toolbox.
At the start of Season 2, Bobbi covers for Fitz's disappearance multiple times when he was searching for a way to find Jemma Simmons. With Simmons missing, Morse and Fitz worked together more in the laboratory. However, this partnership became less frequently as Fitz was absent. Bobbi becomes more concerned for Fitz's absences and asks him to return to the field.
As a desperate attempt to find Simmons, Fitz opens the cage of the Monolith to find her. The team rushes to find Fitz and Coulson berates him for his emotional actions. Morse began to show a caring side to Fitz as she wiped a speck of sand from Fitz cheek. The sand prompted Fitz on a way to find Simmons.
Later, Fitz explained in a meeting that the sand came from an extraterrestrial planet. After Morse volunteers to help Fitz, Coulson notes at this meeting that Bobbi had been covering for Fitz the entire time.
As an attempt to find Simmons, Fitz opens the monolith. Fitz jumps into the portal and Morse and Mackenzie ran to hold the rope keeping Fitz connected to Earth.
BobbiFitz gained a very small portion of popularity before the events of Season 3. In Season 3, Bobbi becomes more caring to Fitz and they both begin to share a brother and sister-like relationship. Many fans prefer this ship to be platonic but has gained a small portion of shippers. Fanfictions around this ship tend to display BobbiFitz's friendship or the pairing in a Soulmate AU.