Hi Atanas,
It may not see straight-forward but since Business Monitoring relies on the Application Monitoring we can get the data we need.
Go to your Business Monitoring

Click in your process and then click in "Analyze Instances"

Just after Group, in the far right click in "API Query </>"

You can see the curl command or the JSON payload, I'm going to use the JSON as body and query the API "all traces" using my API client.
https://instana.github.io/openapi/#operation/getTraces

Now that I have all traces I can request all details from just one trace using the API:
https://instana.github.io/openapi/#operation/getTraceDownload

And then you can do a lot of things from there.
I hope this can help you in your road with the "Business" API.