Parameters are accessed with C4DAtom::GetParameter()/ C4DAtom::SetParameter(). See page_maxonapi_getting_started_foundations_cinema_parameters.
Parameter: Subdivision
MDATA_BRIDGE_SUBDIVISION
Parameter: Tension
MDATA_BRIDGE_TENSION
Parameter: Separate Controls
MDATA_BRIDGE_SEPARATE_CONTROLS
Parameter: Mode Start
MDATA_BRIDGE_FIRST_MODE
Parameter: Mode End
MDATA_BRIDGE_SECOND_MODE
Parameter: Flip Start
MDATA_BRIDGE_FIRST_FLIP
Parameter: Flip End
MDATA_BRIDGE_SECOND_FLIP
Parameter: Mode
MDATA_BRIDGE_BOTH_MODE
Parameter: Flip
MDATA_BRIDGE_BOTH_FLIP
Parameter: Spin Steps
MDATA_BRIDGE_SPIN_STEPS
Parameter: Reverse
MDATA_BRIDGE_REVERSE
Parameter: Restrict to Selection
MDATA_BRIDGE_RESTRICT
Parameter: Patch Mode
MDATA_BRIDGE_USE_SMART_BRIDGE
Parameter: One Sided Patch
MDATA_BRIDGE_ONE_SIDED_PATCH
Parameter: Keep Original
MDATA_BRIDGE_KEEP_POLYGONS