With its world tour theme, it was a revisitation of the concept explored in the duo's acclaimed RCA Victor album, Fancy Meeting You Here, released in 1958. That album had been arranged by Billy May, and he was called upon again to write the charts for this sequel.

As its title implies, the album took popular songs from around the world, but then set them all to Dixieland two-beat arrangements. The songwriters Jay Livingston and Ray Evans supplied the title track and added new lyrics and countermelodies to the other, more-established songs.

Crosby and Clooney were friends, who often performed together on television, radio and stage. That Travelin' Two-Beat was re-released on CD in 2001 on the Collectors' Choice label, combined with another Crosby album from 1965 (this time without Clooney), Bing Crosby Sings the Great Country Hits.

Variety commented: "This parlay of Bing Crosby and Rosemary Clooney results in fair session of Dixieland music pegged to a musical Cook’s tour. While the sound is traditional, the repertoire is definitely offbeat, setting some surprising material into a two-beat format. The duo works with some amusing ideas in the title song, “Knees Up, Mother,” “Roamin’ in the Gloamin’,” “The Daughter of Molly Malone,” “The Poor People of Paris” and “I Get Ideas,” plus a takeout on a Strauss waltz, “New Vienna Woods.” This was the last session produced by Capitol’s a&r exec, the late Si Rady."

Record producer, Ken Barnes, wrote: "This second album, teaming Bing with the delightful Rosemary Clooney, is far less sophisticated than the 1958 classic Fancy Meeting You Here (RCA), but it is enjoyable nonetheless. Like the previous album, Crosby and Clooney have decided to retain the “travel” theme—with songs like “Poor People of Paris,” “Roamin’ in the Gloamin’,” and a clever, up-dated variation of Strauss’s “New Vienna Woods.” The only shortcoming—and with twelve songs it is a considerable one—is that everything is tied to a two-beat Dixieland format. Despite these limitations, Billy May’s tongue-in-cheek backings raise a smile or two. The adaptations and lyrics by Jay Livingston and Ray Evans are very effective. Miss Clooney responds happily to Bing’s bouncy phrasing. If the treatments had been a little more varied and the sound balancing a shade more sympathetic to the voices, this could have been just as good as Fancy."

...
Wikipedia