Feeling confident for an audition is a key ingredient for success.
Certainly the best way to have that confidence is to know the material inside and out. Famous euphonium soloist Harold Brasch did not believe there was such a thing as too much practice. Practice for perfection on everything. Record your practice if possible (see the Recording Your Practice post in this forum). You should also record your own mock audition - play through the entire prepared section in "real time" as you record it. You might also want to have someone else listen to your recording. Better yet would be to have someone listen to you play through the material, taking notes on each piece. Obviously you need an objective listener! Listen to the recording yourself as you look at the music. Are you observing all the dynamics (a common oversight)? Are your rhythms good? Does each tempo match the indications in the music (or common performance practice)? And do you maintain a tempo once you set it? (Compare your ending tempo in a passage with the tempo you started.) Are you playing musically even during the difficult passages?
Above all, don't be intimidated by the others you may hear warming up. Most players tend to play their favorite passages (the ones they sound the best on). They may also play some very difficult etudes that sound really impressive. But they also be avoiding the passages where they sound insecure, even though those passages will be part of the audition. Remember that you can probably also play some pretty impressive passages that may intimidate others. Just focus on preparing everything you will need during the audition and don't worry about the wonderous things you hear from other bells.
Although, I dont sing, I have a passion for acting. I applied to theater songs at various colleges and confidence is key! Of course, I was nervous and doubtful but I felt confident going into the audition and I think that vibe connects with the auditors. Thanks for the suggestions!