Well, several of your desires rule out any drum machine mentioned, and others that weren't mentioned.

If you want at least two variations, MIDI playback and something to create automatic bass lines to what you play, then some form of arranger (module) is the answer. Someone did mention the Ketron Midjay and that would work, albeit fairly expensive.

I still have a Generalmusic WK2MA MIDI Arranger Module that I would sell. It has four intros, variations and endings per style, tap tempo, internal hard drive and floppy drive, 4 part vocal harmonizer, etc. It can function as a simple drum machine or drum and bass accompaniment, or full blown accompaniment. Or you can let it play SMF's that you can play along with. There is also an S-Video output that can display SMF's lyrics on an external TV or LCD monitor. This would really fill all of your requests.