I want to use SauceLabs to test my product that runs across multiple Atlassian server products.
But that's not a URL available external to the container.
So that external testing tools like Sauce Labs can access the running containers.
Although it's not as nice as a built-in feature, it's possible to do this today with Bitbucket Pipelines and ngrok.
You need to sign up on their site to use a "named" subdomain, and either download or install the ngrok client in your build script or use a Docker image which includes it (which I've done below).
change 12345 to match the port you want to tunnel.
I didn't hook ngrok up to anything in the example above, but could see the tunnel successfully connected by checking my ngrok dashboard.
Note that if ngrok is running successfully, no output appears in Pipelines because it is still buffered by the container. There might be some way to prevent the shell buffering the output, but I didn't quite get up to figuring that out yet.
Given the low interest in this feature, we don't have plans to build this any time soon.
For now, the best way is using the ngrok tunnel described above.