I have had hundreds of similar questions from new Instructors and wrote a few articles you may find helpful.
This article includes a number of the other good tips offered here – and a few not mentioned.
This is specific to auditioning for Life Time Fitness – but applies pretty much anywhere.
Just an interviewing tip… look the part. Come in wearing a cycle jersey and shorts, clipless shoes (for whatever the bikes they have support), and ready to give a demo ride as part of your audition. My GM friend says she laughs every time someone shows up in business casual for a fitness position interview when they know a class demo/audition is required.
Harris’s response is great, lots of good contacts. When I was in the business of hiring instructors and trainers, I was always most impressed when an interested instructor would make an appointment to meet with me, then show up, on time, ready to demonstrate his/her skills in working with potential students and/or clients.