Look at Dashboard REST interface.
Build a dashboard which contains the data you want, then use the REST interface to query that dashboard.
There's also a Filter option and thru the filter you can specify the BT of interest.
You can't query the measures directly but what you can do is create dashboards with the data you need and query them for their content using the dashboards and reporting API:
XML is one of the options you can parse, there's also a community plugin for JSON reports haven't tried that through the rest API though so not sure if it works.
https://community.dynatrace.com/community/display/DL/JSON+Reporting+Plugin (requires server restart).
Regardless this is the only option you'll have in AppMon for querying data through the API.