What should you do if you want to get a bachelor's degree in both physics and mathematics?

Make sure you attend a college with both majors and research the requirements for both. Talk to a counselor at the school about how to work out the double-major and declare both. Check and see if any prerequisites apply to both majors and take those classes first.

You must list both as your majors. It will take you about a year, maybe two to do both. Try to get as high a GPA as you can. Apply then to grad school and work towards a PhD. By then you will have to decide which of the two you want the doctorate in. Some very good students are actually recruited by some grad schools. Perhaps you will, also. Also work towards doing well in writing and composition as you will need those as well. Schools are looking for well rounded students.