Deconstructing Warner Brothers
Jamie at Something Old, Something New has had an amazing series of posts analyzing the individual animators within a single cartoon and how you can identify their traits and tendencies. Must be viewed for the artwork.
Most of the next scene with the hillbillies falling for Bugs in drag is Phil DeLara, though Greg says that one close-up shot of Bugs in drag may be Chuck McKimson. DeLara does some fine work on the lecherous hillbillies
Show Biz Bugs
The subsequent xylophone sequence, with the famous "Endearing Young Charms" gag (which writer Warren Foster had previously used in the Private Snafu cartoon Booby Traps and the Bugs/Yosemite Sam scuffle Ballot Box Bunny) is Art Davis. Again, Freleng tended to give him a lot of scenes involving something extreme -- extreme anger or extreme violence, both of which are in this particular scene.
Rabbit of Seville
With Elmer back in the barber chair, Ben Washam animates the sequence where Bugs "is massaging Elmer's head and eventually makes a salad there." Washam also animates the subsequent sequence with Bugs as a snake charmer. Washam is easy to identify, at least in Bugs Bunny cartoons, because he always makes Bugs' teeth pointier -- or "chisel-toothed" as Duffell calls it -- than any other animator, as well as his generally angular way of drawing Bugs's head and features.