@BumbleBeeBoogie,
I don't believe you can catch the flu by ingesting the virus, however if it attaches itself to a bubble that you bring back into your mouth it may have the same effect as if you touched a contaminated area and then put your fingers in your mouth.
I doubt your chances of catching the flu significantly increase if you chew gum and blow bubbles, but anything that increases the opportunity for the virus to get into your nose or mouth will at least slightly increase your chance of being infected.