From the OpenVSP API, the best way to get at the BEM data is through the "BladeElement" analysis. This will place all the data in a BEM file into a ResultsManager data structure which you can easily access from Python.
This is exactly like exporting a BEM file - and then parsing the file into memory -- but in one step and without writing a file.
Once you have the BEM data in memory, I can't help you with what to do in terms of feeding it to SUAVE. To my knowledge, SUAVE does not have any detailed propeller analysis capability like a BEM. Instead, you will likely need to run a separate analysis like XRotor of CCBlade and then parse the results of that analysis to then feed into SUAVE. Even then, I do not know what level of detail SUAVE will deal with propeller data. Ask in the SUAVE Google Group for better answers there.
Alternatively, you can export the BEM file - just like going through the Export menu in the GUI using the normal Export API call passing EXPORT_BEM.
Perhaps you use a tool like XRotor or CCBlade to design a propeller and you want to read that back into OpenVSP. You can import a BEM file (except for the airfoils) through the GUI. Or, you can use the Import call to the API with IMPORT_BEM. At present, there is no way to do the equivalent of IMPORT_BEM directly in-memory from the API.