As I'm new to this stuff, I'm not sure if there are suppose to be small air bubbles in the fuel line while it is running. So far, just breaking it in, and I can see a series of air bubbles consistently flowing through the fuel line. If there is not suppose to be, what could the problem be?

Off the top of my head, I would say make sure that all the pipes are pushed on correctly though saying that - I see bubble from time to time in my fuel lines if I am running on very rough ground.

Check that your fuel tank isn't lose. Also check for any air leaks, air bubbles in fuel tank means air leaks, take out your fuel tank and check it for leaks/cracks, any minor leak, no matter how small it is can cause trouble(running wise and tuning wise) and also try replacing your lines.