Hi,
Sorry, late to reply.
BHI160 integrate BSX, from datasheet description, the maximum odr is 200Hz for virtual sensor, if using pass-through mode, will get BMI160 actual register data. From BHI160 datasheet, you could find raw data to fuser odr is 200hz.

For BMI160 gyro filter, there is no undersampling option for gyro, only normal power mode, for specific bw and odr relationship, you can refer section 2.4.2 in datasheet.
For BMG250, gyro same with bmi160.