Could I get a nose job to just remove my bump?

Yes you can, but you should be aware that removing the bump will leave a flat top to the nose (sometimes called an "open sky"), which many patients don't like.  That's why surgeons often will bring the outer nasal bones in when they remove the bump.  Also, making the bump smaller can change the harmony of the nose.  That's why patients often will also fix the tip when they work on the bump.  IN the end, it's all your choice.  Be sure to discuss your goals and concerns with your board certified plastic surgeon and consider the pros and the cons. Be certain your surgeon is properly certified.  I've attached a link where you can start your search. 

Hello and thank you for your question. Based on your
photograph, you may benefit from a conservative dorsal hump reduction.  Make sure you specifically look at before and after
pictures of real patients who have had this surgery performed by your surgeon
and not just a computer animation system. The most important
aspect is to find a surgeon you are comfortable with. I recommend that you seek
consultation with a qualified board-certified plastic surgeon who can evaluate
you in person.
Best wishes and good luck.
Richard G. Reish, M.D.
Harvard-trained plastic surgeon

Removing a dorsal hump is typically a very straightforward part of a rhinoplasty (nose job), and can sometimes be done in isolation without altering other parts of the nasal anatomy.  A visit to a plastic surgeon's office will help you to understand if you're a candidate for the procedure, and what aesthetic outcomes are realistic in your particular case.  In order to get a qualified, ethical, and expert opinion on your surgical options and expectations, schedule an in-person office consultation with a plastic surgeon certified by the American Board of Plastic Surgery.
Best of luck,
Keith M. Blechman, MD
New York, NY