I'm playing on the Xbox 360, and I'm at the part in the Imperial civil war questline where I have to regain Winterhold. I've gotten the orders from Tullius to report to Rikke, but she won't give me the dialog option "reporting for duty" to advance in the questline. Any idea how I fix this?

Is the quest marker on her? If not check your journal to be sure it is time to report to her.

Idk if it's the right part but I know you won't get reporting for duty option on both sides without putting on the officers armor they gave you. I'd try that

Yes, the marker is on her. As for the officer armor, where do i get some?

I've never worn officer armor, Legion or Stormcloak yet I've beaten both sides multiple times.

I have the same bug, i'm trying to do the

This bug has been known since 2011, I also have it, and nobody has been able to tell WHY this is the case or how to really fix it.

Okay, I've gone back 7 hours before I completed the game, and am going again from there. This time, I'll retake the Rift first. Kind of bad Beth hasn't fixed this...

Happened to me, I installed the game to my HDD and it worked. Make sure you go to Castle Dour and exhaust the "How goes the war" dialogue option with General Tullius, then try returning and speaking to Rikke. Also try discussing the other dialogue options she has several times each and it might appear.