It's not an album I've got but I would have been surprised to find Ben Webster playing bari or clarinet. However, a quick look at the version for sale on Amazon has mp3 clips that are listed as Harry Carney leading. I did listen to a couple of the Ben Webster clips and I'm with Rhys. Ben's playing stands out on its own and the strings don't add anything (other than commercialism). The same goes, in my view, for others "with strings" - Billie Holiday, Charlie Parker.
Ben Webster started on violin and moved to piano before taking up the sax. There are some examples of his piano playing on the cd version of his quintet album Soulville.
While on Ben Webster, I recently bought the complete Ben Webster/Harry Edison/Billie Holiday cd set. It contains a beautiful version of "We'll Be Together Again", which is also listed on the Music For Loving album. In his own way, Ben Webster was amost as perfect a foil for Billie Holiday in the 1950s as Lester Young was in the 1930s.
YC