Both sides can be heard now on YouTube and definitely do not have the Tab Smith orchestra accompaniment (trumpets, alto sax, piano, bass, drums) listed as "probably" on jazzdisco.org. Instead I hear a xylophone or glockenspiel and an electric guitar besides the featured vocal trio, The Three Riffs (Eddie Parton, Joel McGhee and Bunny Walker).
Uploaded record label shows that the Jazz Discography Project website was not correct in indicating the song title as "Bewitched, Bothered and Bewildered". In fact it was just "Bewildered", as originally entered here (and meanwhile corrected on jazzdisco.org as well). The uploaded clipping from the Billboard Dec 4, 1948 issue also shows that Atlantic first viewed this cover of the Red Miller Trio's record on Bullet 295 as the top side. Obviously it was a rush release, put on the market only a few days after its recording on Nov 23, 1948 and advertised in the same Billboard issue as the Bullet record (which could at least argue "Why wait for substitutes - Get the one and only original"). The Atlantic single was pressed so hastily that they didn't take the time to check the composer credits which are missing on the record label. The song was actually written already in 1936 by Teddy Powell and Leonard Whitcup and was a hit in 1938 for Tommy Dorsey and His Orchestra.
The Jazz Discography Project website indicates an accompaniment by Tab Smith's orchestra. They have the title down as "Bewitched, Bothered and Bewildered".