What steps do I need to take?I need to figure out how to get this resolved quickly so I can pass a background check for work.

Well I hope you understand the reckless driving is a criminal charge it's not really a traffic citation. Huge mistake missing that court date. Are you sure about that speed 15 over the posted limit? Where you over 80 mph? Possible you will never get it off of now permanent criminal record. You're only reasonable option forward is to meet immediately with a traffic attorney in your area and discuss what if any options you have, whether there is a warrant out for your arrest, and what your best way forward is.

You need t speak with a traffic attorney about what your options are. If you were found guilty of both charges, you may be stuck with 2 criminal misdemeanors on your record.