You should be able to get and set the tempo map from the BB Plugin in Reaper with API:

Count DAW tempo markers for BB plugin:
int CountTempoTimeSigMarkers(ReaProject* proj )

Get DAW tempo map for BB plugin:
bool GetTempoTimeSigMarker(ReaProject* proj, int ptidx, double* timeposOut, int* measureposOut, double* beatposOut, double* bpmOut, int* timesig_numOut, int* timesig_denomOut, bool* lineartempoOut )

Add tempo markers to DAW from BB Plugin tempo map:
bool AddTempoTimeSigMarker(ReaProject* proj, double timepos, double bpm, int timesig_num, int timesig_denom, bool lineartempochange )

Same with Chords:
int AddProjectMarker2(ReaProject* proj, bool isrgn, double pos, double rgnend, const char* name, int wantidx, int color )

ReaTrak Biab & Plugin in Reaper
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