BASS doesn't have access to the final mix - it's mixed by the hardware (or DirectSound if the device has no hardware mixing). But there a couple of ways to do what you're asking...
1. Record the sound, using BASS_ChannelGetLevel(RECORDCHAN) to get the level. The good side is it takes minimal effort/processing, the bad side is that it'll include the sounds from all apps using the device. Also, some old soundcards don't have "what you hear" or "wave" type of recording inputs.
2. Use BASS_ChannelGetLevel on each of your playing channels (scale each by the channel's volume), and add them all together to get a total level. The good side is it only measures your app's sounds, the bad side is it requires a bit more processing.
Personally, I'd use method 2