The trial of Heather Cook for the manslaughter of cyclist Thomas Palermo is to start on Thursday and is expected to be postponed for some time by the judge.
Lawyers for both sides will ask the judge for more time to prepare cases, it's expected.
The 58-year-old, who's pleaded not guilty, was removed as Episcopal Bishop of Maryland after the incident in December.
Ms Cook has admitted driving the car that hit the cyclist.
Prosecutors accuse her of manslaughter, leaving the scene, driving under the influence of alcohol and texting while driving.
Speaking in April, as a court date was set, the former bishop's lawyer said: "Our thoughts and prayers are with the Palermo family.
"Ms. Cook can't say anything based on the legal situation and the advice of counsel, but we are all saying our prayers. It's a horrible situation and we will be in court June 4."
The cyclists sister Alisa Rock said: "We know this is the first step in a long process, so we are looking forward to having this resolved and to see justice."