Hey Thomas, welcome to the Atlassian Developer Community!
We have a tutorial for getting started with Bitbucket Cloud and node.js. Once you’ve set up the initial server, you could modify it to serve React on your HTML pages. Once you’re done with that, you can import Atlaskit the same way you would on any other webpage.
There’s a great template repository I found on the Community site that might also help clarify how you’d implement that with atlassian-connect-express.
Good luck, and enjoy your stay!