The tremolo should work just as well on bass as it does on guitar. All the coupling caps are more than big enough to pass the bass frequencies.
An active bass will work perfectly well with the Trem providing it does not have an absolutely huge output. But then any active bass with a very high output is likely not to work with other pedals too.
The Tremolo is a really good sounding trem - it does not have a huge range or lots of fancy features, but what it does it does very well.
I built a strip board version -http://www.buildyourownclone.com/board/viewtopic.php?f=8&t=36794