I think the problem you're experiencing stems from two issues:
(1) You can't record your own bass part using the Split Voice, because you can't record the Split Voice at all (see page 31, "Limitations while recording").
However, that's if you're using the keyboard's Song Sequencer to record. If you record your keyboard's audio or MIDI output using external software (e.g., a DAW) or hardware (e.g., recording equipment) then you will be able to record the Split Voice if you want-- although you still won't be able to play the Split Voice at the same time as an Accompaniment (at least, not without hacking a Registration to create two different Split Points).
If you want to record your own bass part using the keyboard's Song Sequencer, you can record it using the Main Voice-- e.g., record yourself playing a piano part on one track using the Main Voice, then change the Main Voice to the desired bass sound and record yourself playing the bass part on a different track while the piano track is playing back. To do that you must be sure to select the specific track you want to record the second part on, as described on page 31. The drawback is that you can't record the two parts (piano and bass, or whatever two instrument sounds you're using) at the same time as each other, although this is actually the way most songs are recorded in a studio-- each track is recorded separately, in time with any previously-recorded tracks.
You can also record the Bass track of the Accompaniment, which is what Ted was describing in his step-by-step instructions. An Accompaniment is composed of up to six tracks (or eight MIDI channels), and you can turn each track on or off using the procedure described on page 45. Thus, after you press the REC button but before you start to play, you can press the track 3 button to turn off the Chord 1 track, press the track 4 button to turn off the Chord 2 track, press the track 5 button to turn off the Pad track, and press the track 6 button to turn off the Phrases track. Then the only tracks of the Accompaniment that will play will be the Drums track and the Bass track. But you won't be able to select the bass voice for the Bass track, because the voice selection is built into the Accompaniment. Likewise, you won't be able to play your own bass riffs, because the notes for the Bass track are also built into the Accompaniment and all you can do is control the chord they're based on.
(2) The Accompaniment's Drums track will start to play as soon as you press the START/STOP button as mentioned on page 30, rather than waiting for you to begin playing-- and if you press a key in the Accompaniment section of the keyboard, the other Accompaniment tracks will start to play as well.
If you want to record just the Drums track by pressing the START/STOP button, you can let them record by themselves for a measure or two-- i.e., as an intro-- before you start to play and record the piano part. However, you'll need to avoid pressing any keys in the Accompaniment section to the left of the Split Point, otherwise the other tracks of the Accompaniment will start to play as well-- unless you've turned them off as described on page 45.
Alternately, you could turn off all of the Accompaniment tracks except for the Drums track, and record yourself playing just the piano part, letting the Accompaniment start automatically when you start to play. You'll need to avoid pressing the START/STOP button first, but at least you won't need to worry about accidentally hitting a key in the Accompaniment section.
Another alternative is to record your own drums part to a specific track, as mentioned above for the bass part-- i.e., select one of the Drum Kits for the Main Voice, or perhaps an instrument sound from the Percussion category on page 4 of the Data List, or from the XG Percussive category on page 8 of the Data List, etc., and then play the drums or other percussion/rhythm instrument yourself. This gives you the freedom to pick your own sounds, as opposed to being stuck with whatever is built into the Accompaniment. The drawback is that you have to keep time yourself-- although that can be a good thing, because it lets you slow down, speed up, pause, etc., as desired, and the rhythm will sound more human and less robotic.