Don't Let Notes Overlap. Most bass lines are single notes, and because bassists lift fingers, mute strings, and pick, there's going to be a space between notes. Go through your MIDI sequence note by note, and make sure that no note extends over another note's attack.
The orange notes have overhanging decays and attacks. The gray notes to the left and right have had their lengths trimmed to prevent overhang.
Limit MIDI velocity. Really great bass players are known for their "touch"—the ability to play notes consistently, in terms of timing and dynamics. In some ways, it can be harder to play keyboard notes consistently than bass strings, but the MIDI velocity limiting technique presented in yesterday's tip is a fine solution.
Use slides. Real bass players use a lot of slides in their playing, and using pitch bend to create slides can benefit MIDI bass as well. Set the bass synth's pitch bend range to plus and minus a fifth or an octave, depending how much of a slide you want—I use
Take advantage of synth parameters. Use velocity not only to control dynamics, but brightness—have the filter cutoff lower at lower velocities, and higher at higher velocities so that hitting the keys harder creates a brighter sound.
For really realistic bass parts, check out the IK Multimedia MODO bass.
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