Hey, so a few people in trade chat and I spent hours yesterday testing things for this bug (I am on Blackrock Alliance myself). Here is what we found so far:
Starting a brand new character and going through Exile’s Reach, upon reaching Stormwind and SKIPPING the tour at the beginning, we were unable to get the quest to do BfA. The text when selecting to skip the tour does say select a timewalking campaign, but I can’t imagine they mean to lock you out.
Since I skipped the tour, I tried to find Jaina or Mathias in SW and accept the quest that way, no luck.
I took the boat to Boralus and searched all of the city. i could pick up side quests in some areas, but not start the campaign.
I walked out to Silithus and checked with Magni, but he wouldn’t talk to me and I could not use the portal.
I also tried talking to Chromie, timewalking to a different campaign, then ‘returning’ to my current timeline, nothing ever changed.
I then tried all of the steps listed above with my old Paladin on another server, one who was part way through WoD and is now 42, and he also was not able to start the BfA campaign.
After this I decided to go and reroll my new character, except when I got to SW I elected to take the tour. After the tour was over, I immediately received the quest to go meet in the keep and then go meet Jaina and head to Kul Tiras.
Another player (Blackvain-AzjolNerub) and I tested during this time my ability to share quests with him or to follow me and hopefully find where it starts. I was unable to share any quest with him up until the point I started receiving gathering quests for Ashvane Trading Company, and at this point we have stopped testing.
So, note to people rolling new characters that want to do BfA, TAKE THE TOUR. Hope this helps