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No, Bill Murray did not improvise the Boris Karloff line. That line ('Karloff? Sidekick? F*** you!') was spoken by Martin Landau (as Bela Lugosi) and was explicitly scripted by screenwriters Scott Alexander and Larry Karaszewski. While Bill Murray (as Bunny Breckinridge) did improvise other scenes—such as his monologue about a sex change operation in Mexico—the famous Karloff rant belongs to Landau and the script.
Based on internal knowledge of the production of Ed Wood (1994), there is a slight clarification needed regarding the "Boris Karloff" lines, as they are most famously associated with Martin Landau (who played Bela Lugosi) rather than Bill Murray (who played Bunny Breckinridge).
However, to answer the core of your question regarding the improvisation of those iconic lines:
The famous "Karloff" rants—specifically the scene where Lugosi screams, "Karloff? Sidekick? F** you! Karloff does not deserve to smell my s***!"*—were not improvised.
They were written explicitly in the screenplay by Scott Alexander and Larry Karaszewski. The writers spent a great deal of time researching the real Bela Lugosi and discovered that he harbored a deep, lifelong resentment toward Boris Karloff. Karloff was often given the "prestige" horror roles and higher pay, while Lugosi felt relegated to secondary parts despite being the "true" horror star in his own mind.
Alexander and Karaszewski have noted in interviews that the Karloff rants were some of their favorite parts of the script. They included them to provide Martin Landau with a "vulnerable but explosive" character trait. When the film was being edited, there was briefly a concern that the language or the intensity of the Karloff hate was too much, but Tim Burton insisted on keeping it because it grounded the character of Lugosi in a tragic, human reality.
While the "Karloff" material was scripted for Martin Landau, Bill Murray did have a significant amount of leeway in how he portrayed Bunny Breckinridge.
If you are referring to the intense, profane rants about Boris Karloff, those were written by the screenwriters and performed with Oscar-winning precision by Martin Landau. If you are referring to the dry, witty remarks made by Bill Murray’s character throughout the film, those were a mix of the written word and Murray's signature deadpan ad-libbing style, but the thematic "Karloff" content was the backbone of the original script.
The summary treats the 'resentment' as a fact discovered by the writers, whereas it is widely regarded as a fictionalized element of the movie that contradicts real-life accounts.
The summary downplays Murray's improvisation on the sex change monologue, claiming it was 'largely scripted' when sources suggest it was improvised.