Can we create a BDM via API
If I understand correctly you want to save some business data without going through the execution of a process. A process allow you to save business data using business variable default value or operations on tasks.
Saving business data is not possible using Bonita API. As you figure out you have only a read access to business data.
The solution I would suggest is to have a very basic process definition with a contract to get the data and a business variable with a default value to trigger the persistence in the database. You can then instantiate this process (and provide data to be used by the contract) in a single API call.