PARK CITY, Utah (AP) _ Actor Robert Stack and director Budd Boetticher were to be on hand tonight for a showing of the restored version of ''The Bullfighter and the Lady'' at the United States Film Festival.

The print to be shown is the ''director's cut,'' the version Boetticher turned over to Republic Pictures. With a running time of over 120 minutes, the studio felt the film was too long and excised 40 minutes of it before it was released in 1951.

In the film, Stack plays an American who travels to Mexico to learn the art of bullfighting.

The film's restoration was directed by Robert Gritt of the UCLA Film and Television Archive.

The festival, sponsored by actor Robert Redford's Sundance Institute and the Utah Film Development Office, opened Friday and continues through Sunday.

Film students from the University of Utah, Brigham Young University and the Salt Lake High School Media TV Arts Program were given a private showing Monday of ''My Little Girl,'' a film in the independent dramatic competition starring Geraldine Page, James Earl Jones and Mary Stuart Masterson.

The students then attended a seminar on ''Students In Film - Where Do We Go From Here?'' The session included actress Jane Alexander, whose ''Square Dance'' opened the festival; Randa Haines, director of ''Children of a Lesser God''; and Sterling VanWagenen, producer of ''The Trip to Bountiful.''

''Robert Redford is very enthusiastic about this new program and wants to see it expanded in future years,'' said festival spokeswoman Saundra Saperstein.