Was too much cartilage added to the bridge of my nose? Or is this extra swelling? How would I fix if the bump stays? (Photo)

You are not near a final result at 3 weeks after surgery.  Be patience and follow your doctors advice about taping and allow the tissues to settle and mature over several months.  If a small bump is still there in 9-12 months it can be dealt with by a small revision without any worry about disrupting the other parts of your rhinoplasty.

Thank you for your question.
Without an in person examination it is impossible to give very accurate advice. In general at three weeks it is very early in the healing phase to know what your nose will look like. In my rhinoplasty surgeries I expect some swelling of the dorsum and it would be better to have it slightly full at three weeks than looking perfect as in time the swelling can go down further and the bridge could end up too low. Please address your concerns with your surgeon.
Hope this helps-
Dr. Wayne

It is too soon after your surgery. This could be swelling and it is possible that it is going to go away. Should it not disappear after about a year your surgeon can remove this fullness and it will not require a doing everything over again.