Born in Siena, Bastianini first began performing at fifteen while apprenticed to a pastry chef, Gaetano Vanni, who discovered his vocal talent and encouraged him to join the choir of his hometown's cathedral.
Among his roles that year were his first performances of Zio Bonzo in Madama Butterfly, Don Basilio in Il barbiere di Siviglia and Sparafucile in Rigoletto.
In 1947, Bastianini toured Egypt, singing in Cairo, Alexandria and Giza, sharing the stage with baritone Gino Bechi and soprano Maria Caniglia, reprising the roles of Don Basilio and Sparafucile.
In 1949, he toured Egypt again and flew to Caracas, Venezuela to sing in productions of Aida (Ramfis), La bohème, Lucia di Lammermoor and Rigoletto.
Believing his voice was better suited to the baritone repertoire and encouraged by his teacher, Luciano Bettarini, Bastianini left the stage for seven months, studying and re-training his vocal instrument.
In 1953, Bastianini performed opposite Maria Callas in the first of many pairings with her, as Enrico Ashton in Lucia di Lammermoor at the Teatro Comunale Florence.
That same year he sang the role of Carlo Gérard in Umberto Giordano's Andrea Chénier for the first time at the Teatro Regio di Torino.
He made his Metropolitan Opera debut as Germont on 5 December 1953, opposite Licia Albanese as Violetta and Richard Tucker as Alfredo.
On 10 May 1954 he made his debut as a baritone at La Scala, in the title role of Tchaikovsky's Eugene Onegin, with Renata Tebaldi as Tatyana.
On 31 October 1955 (opening night), he debuted with the Lyric Opera of Chicago as Riccardo Forth in Vincenzo Bellini's I puritani with Callas as Elvira, di Stefano as Arturo, and Nicola Rossi-Lemeni as Giorgio.
He sang regularly in Chicago between 1955 and 1958, as Conte di Luna (opposite Jussi Björling and Herva Nelli), Don Carlo, Germont and Marcello.
After leaving the Met in May 1957, Bastianini made his first appearance on Italian television in a filmed version of Il trovatore with Leyla Gencer, Mario del Monaco and Fedora Barbieri.
That summer, he sang Don Carlo in a legendary production of Verdi's Ernani at the Maggio Musicale Fiorentino under Dimitri Mitropoulos with Anita Cerquetti, Mario del Monaco and Boris Christoff.
This was followed by performances in four different operas in seven days in Bilbao and a return to La Scala in December 1957 for another lauded production: Un ballo in maschera under Gianandrea Gavazzeni with Callas, Di Stefano, and Giulietta Simionato.
In July of that year, he made his debut at the Salzburg Festival as Rodrigo under Herbert von Karajan, and then returned to Bilbao in September for several more performances.
The following December, he sang his first Michonnet in Francesco Cilea's Adriana Lecouvreur at the Teatro di San Carlo, starring Magda Olivero.
Later that month he appeared in two productions at La Scala, Lucia di Lammermoor with Dame Joan Sutherland and I puritani with Renata Scotto.
Also noteworthy is a 1955 television appearance (published on DVD in 2006) on Opera Cameos of excerpts from La traviata with the young Beverly Sills and Paul Knowles.