The duration is available from BASS_ChannelGetLength, like this...
QWORD length=BASS_ChannelGetLength(handle, BASS_POS_BYTE); // get length in bytes
double secs=BASS_ChannelBytes2Seconds(handle, length); // translate that to seconds
The average bitrate can be calculated by dividing the file size by the duration, like this...
QWORD filesize=BASS_StreamGetFilePosition(handle, BASS_FILEPOS_END); // get file size
double bitrate=filesize*8/secs; // calculate average bitrate (bps)
Also see BASS_ChannelGetInfo and BASS_ChannelGetTags for other information that's available.