Eh. I'll weigh in on this one, but take it for what it's worth- I'm not a competitive bodybuilder and I don't know what it takes. I am, however, an advanced, competitive Brazilian Jiu Jitsu purple belt. The dedication is probably similar in many ways; I train BJJ for 2 hours 4x a week, require strength and conditioning 3x weekly, and need a pretty formidable nutrition approach to keep up. Coupled with weight management (low bodyfat, more muscle is obviously a competitve advantage) and the time investment is considerable.
My fiance deals with me having a full time career, 8 hours of time investment in Jits alone (mostly evening classes that go as late as 10pm) and all the extras (including numerous injuries). Without someone who is supportive, I would have to settle for only training 2-3x weekly total. It just wouldn't work in most relationships- very few women like the idea of you spending this much time away. But she and I invest our time carefully- most couples' idea of quality time is watching ****ty weeknight reruns or shows they've never heard of on Netflix. When we spend time together, it's "active" and fulfilling; we talk, we make dinner together (esp. when im cutting weight) and get more out of the time we DO spend together. This might be an area for you guys to consider; if she's not an active gym goer herself, and if she's filling the spare time with mundane sedentary activities, how do you guys spend time? If it's quantity over quality, then that may partially explain why she's opposed.
I think there's more to look into than black and white, dump her or quit, etc. You said you're happy with her; will you two be able to figure out a common ground where you can be successful and competitve and she can be happy w/ the relationship? I think so. You're not asking her to stand next to you on stage, you're asking for support. Honestly, when all else fails, just do it and she'll get over it or used it.