My hubs keeps his shoes on his pedals, runs barefoot to the mount line, does a flying mount and puts his shoes on as he rides.

Ummm yeah... I'm FAR too clumsy to try all that.
7 years of doing tris and I *still* put my shoes on in transition, run to the mount line, stop to get on my bike and then pedal way. I figure the 20 seconds it costs me to do it this way is surely less than the 4 hour trip to the emergency room that would result if I tried to mount my bike running and put my shoes on while riding.
My shoes aren't too easy to run in, but it doesn't matter. You just clip clop your way to the mount line, saddle up, and get on your way.

Good luck at your first tri. There's truly nothing like it!!