Electrical engineering, acoustics, psychoacoustics, woodworking, computers. Not that you necessarily need degrees in all of these, but they all come into play (imho anyway).
Unless you can find a cirriculum that fits your goal, or a good academic advisor who will help you tailor one, much of what you need you'll have to learn on your own.
Here is some of the self-education part:
1. Go to the Eminence website, click on "Resources" and read everything that looks like it might apply.
2. Get "The Loudspeaker Design Cookbook", by Vance Dickason, and read it. Yeah it's about home audio, but the principles apply to bass cabs too.
3. Get "Premium Home Theater: Design and Construction", by Earl Geddes. Ignore the video chapters; the acoustics and psychoacoutics chapters are what you want.
4. While you're waiting for those books to arrive, search Talkbass for posts in the Amps section by BillFitzmaurice and greenboy. Read the ones that look applicable.
5. Join the Audio Engineering Society, and dive into their library. Start with early articles on loudspeakers, like back in the late 40's. The early articles are less math-intensive than the later ones.
6. If you speak calculus, I also recommend "Transducers", by Earl Geddes.
7. Select a loudspeaker design software package, and the hardware you need to go with it. I use the Linear X suite of software, but it's kinda pricey.
8. You need to be able to measure a woofer's Thiele/Small Parameters and frequency response on your own, because woofers don't necessarily match their published specs (and some models are way, way off). And nothing really matches its published frequency response curve. Anyway, make sure such T/S measurement capability is included in your software/hardware package or purchase something like the Smith & Larsen woofer tester.
9. Bunch more good books here: Invalid Link Removed, to go "shopping" and then "books".
10. This is self-education that doesn't come from a book: Have a mission, a sense of purpose, instead of just a goal. If you don't yet, then start looking for it.
11. Be friends with your competitors. It's a big enough pond that the fishermen can all get along.
12. Possible alternative to 7 and 8: Hire a professional to do the design work for you, and concentrate on the produciton side. But the more you know, the better off you'll be.
Best of luck to you,
Duke