Justice Gilbert said although he had never met Mrs Busch, he was part of a legal firm that acted for the lion park: "The legal position is that I must recuse myself if the circumstances give rise to an apprehension of bias."
He said a reasonable person would be concerned about his involvement in the matter.
Although he could not hear the case, he was happy to talk to Mrs Busch about what another judge may do in terms of dealing with the case.
Mrs Busch represented herself because she had been unable to secure legal aid as of yesterday morning.
Justice Gilbert offered three dates - April 29 and 30 and May 2 - before adjourning the case.
Mrs Busch chose April 30, saying it would give her ample time to travel from Karapiro, where she lived.
She has been embroiled in countless legal battles, particularly with her son and Lion Man Craig Busch.
Both came together in a High Court-initiated discussion last July but talks between them are on-going.