Blizzard gives us a breakdown of all your options
[[Update: The pre-patch is now live and you can begin the process of transferring your characters between each classic game. This is what your launcher will look like in the future. There is an option for 'Burning Crusade Classic' as well as 'World of Warcraft Classic'.
Upon logging in, I was able to make the switch and it was relatively painless. After changing one of my druids to Burning Crusade, the game told me I could clone my character in WoW Classic for $15 at a later date, which I chose not to. Quite simple!
I have to say, looking aside for clone fees, this really brings me back to revisiting the Dark Portal splash screen.]
WoW Classic is about to be split in two.
On one side of the Dark Portal: Classic Classic. On the other, Burning Crusade Classic. We knew this day would come and for months we tried to figure out how it would actually work. But just recently, via Blizzard's BlizzConline stream, we know how it will work. And that involves two completely different servers.
When May 18 rolls around, the “pre-expansion patch” will go live in Classic. At this point, you'll have two choices: you can advance them into the new expansion or stay in the old hotness (which will get confused in the new "old" servers). Or, you can “clone” them for a fee.
Blizzard is now ready to explain in detail how it will all work, through this detailed blog post here. Here's the gist of the clone: "Upon installing and logging into the other game, in this case World of Warcraft Classic, you'll see [your character] listed and is grayed out. The text under his name now reads: “Clone available”. A Clone icon will appear next to Thuata's name as shown below. A tip will appear when hovering over the Clone icon with the mouse. If you click on the Clone icon, a confirmation window with more information will appear. It shows the "cloned" date of the character which includes all progress on the character up to that date. “Then you pay the fees, and you're good to go.
Between the video below and this full recap, you should be ready to tune in on May 18 and plan your course. As a reminder, Blizzard recently changed the price for character cloning from $35 to $15.
I plan to push everything forward, if Blizzard continues this process of pursuing expansions. It's a lot less overhead and I don't mind slowly replaying the game's progression style once again.
Playing Ahead: Making Choices in WoW Classic [Battle.net]