Outsideof software like Trillian, you'll need to have essentially two things going:
1) A bass sound that acts like a bass
2) A midi sequence (played and/or drawn) that incorporates the dynamics you're looking for
For 1, you start off by finding a bass sound that gets you at least part way there, and ideally responds to dynamics (e.g. velocity). Ideally, you want to use a synth that supports a lot of modulation options, such as many to many modulation routing.
To sound more organic, you can tweak the modulation routing to subtly alter the tone in response to dynamics. You generally want all of this additional modulate to be very subtle, just barely perceptible. Set the level of modulations high while you're tweaking the settings, and then bring the modulation levels down to taste so that you get a very subtle effect that isn't overbearing, and perhaps barely perceptible at all.
Here are some examples of ways that you can modulate a sound to make it more 'organic' dynamically:
Use velocity to modulate the level of a pitch envelope with an immediate attack and a very short decay. This can help emulate the quality of a bass string settling into a stable pitch after being tweaked. You want this effect to be subtle.
You can also add an extremely quick shot of noise to the attack, if that seems to be lacking. There's a couple ways to do this, but I like to modulate the pitch of the oscillator with a very very quick burst of noise, if that's supported by the synth. You can also modulate the amplitude and pitch of a noise oscilator or layer another synth sound that's comprised of just noise. Modulate the pitch and amplitude envelopes for the noise with velocity here too, with an immediate attack on the envelopes and a very short decay (as per above, but maybe even faster, tweak to taste).
You can also use velocity to modulate the cutoff of the filter(s). A harder note should have more high end frequencies and less low end frequencies in the sound. If you can apply multiple filters to a sound then use a high-pass filter that's initially let's all of your low frequencies through (so it basically has not effect on the sound at all to start with) and then another filter or set of filters that you probably used to get your bass sound (low-pass, band-pass, or waveshaper, whatever). Then modulate the cutoff of both filters up a bit for higher velocities. You can also modulate the resonance a bit the same way, which works well too. Again, set the modulation amount high to get an idea of what's happening and then dial the modulation way back until it's just a very subtle effect.
Also, and this is often overlooked, pitch bend should not just bend the pitch! When you bend a real bass string, the pitch, frequency content, and amplitude of the vibration are all affected. So, just like velocity can/should modulate a number of different aspects of the sound, pitch bend should also subtlety increase the filter cutoff/resonance (to make a sound a bit thinner and/or more resonant) and either increase or decrease amplitude (whatever works best for a given case).
You can also layer multiple sounds such that different velocities and/or some controller like a modulation wheel/strip/IR beam or foot controller will trigger different sounds/variations of a sound. For example, to mix a slap bass sound with a 'regular' fingered sound, you can crossfade between the two sounds (or more variations!) using a modulation wheel or other controller (or just draw the crossfade in your track). Trillian triggers different bass sounds (pluck, slap, pinch, etc.) by assigning them to different midi channels, but I think it's easier to use a controller or automation envelope to do this.
For number 2, you'll want to study and understand how a bass is played. Not every single note is plucked, and there can be a lot of legato playing. One thing that can help with this is to think of a bass as four (or more!) keyboards stacked on top of one another, with only about four to five notes easily reachable at any given keyboard 'position' at any given moment. Also importantly, unlike with piano, it's very easy and common to repeat a single note without the note turning 'off' like when you lift your finger off the keyboard. If you use a sustain pedal, you can easily emulate this dynamic, just hold it down when you want to emulate a bass player fingering the same note with their plucking hand and then let go when you want to 'mute' the release of the notes.