Kate Bush does not enjoy playing live, to put it mildly. Her only actual tour came way back in 1979, and it lasted just 24 shows. Since then she's declined ridiculously lucrative offers for tours, opting to focus entirely on her albums and her family life. In the Eighties she did agree to play briefly at huge events like the Prince's Trust, Comic Relief and The Secret Policeman's Ball, but those were isolated events.
David Gilmour is a regular road rat next to Kate Bush, though his shows are also very infrequent. In January of 2002 he staged a series of concerts at London's Royal Festival Hall, and Bush came onstage to perform the Roger Waters vocal parts from "Comfortably Numb" during the second night. Gilmour is probably the one person who could have coaxed Bush onstage: He essentially discovered her when she was 16 years old, and he helped her cut her first professional demo and used his connections to get her signed to EMI.
Sadly, there's no professionally shot video of their duet, but this amateur footage is watchable enough. Gilmour launched a brief world tour four years later, but Bush has yet to play live again in any capacity. Rumors swirled last year that she would appear at the Olympics Closing Ceremony in London, but they ultimately just used her new recording of "Running Up That Hill" while a large group of drummers and dancers performed. Bush has said a number of times she'd like to play a short tour someday, but we'll believe it when it happens.