What happens if a customer has already added the product in the cart that I was going to show as a bump offer?

In this case, you can skip the bump offer. To do this, go to the “Global Settings” of the Order Bump plugin. There you’ll find a feature called, “Skip for Same Offers.” Click on the dropdown in front of it, select Yes, and save changes. 

Now if a customer has added an order bump offer product in the cart, the funnel won’t trigger.