I have to bike in my road shoes, because I have SpeedPlays and I can't pedal with running shoes.
You get more power on the bike with clipless pedals.
So, I wear my bike shoes out of T1 and my running shoes out of T2.
It's all about what you are comfortable with though. I see many people who use their running shoes on the bike and run.
Best of luck! Let us know how it goes.
"Life is not a journey to the grave with the intention of arriving safely in a pretty and well preserved body, but rather, to skid in broadside thoroughly used-up, totally worn out, and loudly proclaiming: WOW WHAT A RIDE!!!!"