The MIDI approach also allows you to use all of your audio FX on the output (same as if it were a live bass, but allows you to change your mind later on), so do not feel constrained by the samples or VSTi you use. Running an amp sim on the output is a convenient way to get an FX chain on the tail end (often best if you use a clean sample set feeding it).
 
Although using MIDI at first may be a bit awkward, bass is one of the "timing masters" in a tune and will allow you to insert tempo changes readily as you build a song up (tempo maps will automatically adjust the MIDI).

chuckebaby
Some great ideas on this thread. I also Dupe Bass tracks with Synth bass as well.
The one thing that Melodyne fails to do well is velocity changes.
I do a lot of hand muting with bass and sometimes an occasion fast attacking notes.
Melodyne has no clue when it comes to those two things. Some hand work is necessary. IE- Fine tuning.
 
This is a good example of doubling a Fender P-Bass with a Midi Synth bass. Listen to the intro-
https://soundcloud.com/charlie-roy/seven
 
P-Bass Is direct/clean. Synth Bass has saturation/dirty.
Probably not your cup of tea but that's how I do it.

Wow!   Talk about punchy!!!   Great for that style, but not for my country tune...
 
 

Cactus Music
You missed the comment above by Mettelus. You need to process/transpose +12 
 
The down side of this whole idea is if your not adept at midi editing you will have a whole new world to learn which might be daunting at first. Some of us it's second nature as we been at it since Cakewalk was only midi. So the results will depend on your midi editing chops.  

OK, John, did it successfully.  Thanks! 
 
I can see the benefits...  just grouped a whole lot of midi notes and shortened them however I want... very cool. The sustain on the bass line was what was ruining (muddying) the track. Not sure of the quality of tones coming from SI- Bass yet, will take some fudging. 
 
But it seems you pretty much have to go thru it note by note, as the timing seems to have changed as well... don't want to quantize or change note lengths to sterility... lots of time and patience required here. 

There are thousands of bass VST possibilities out there. I'm sure there are many better than SI Bass but I found the Jazz Bass patch and I added more compression sounds not bad for how I use it. If you have the time trying other bass VST's might be worth it as once you find the one you do like your more or less set for life. 
I find many of the bass sounds are what I call a tuned fart. Not even close. 
 
And another important trick to try while your in midi world is take the kick drum audio track and use drum replacer to convert it to midi. You can drag that track to it's own midi track too. Then undo the regional effect on the audio track and leave it as audio. I end up using the Midi kick track 90% of the time. 
Now you can use that midi drum track to tighten up timing of the bass notes.
Open the Kick midi track then while holding CTRL open the Bass midi track. Now you can see both midi tracks and line things up. 
 
I'm finding the combination of using some midi tracks that were from the live session and converted really sparks up a song. 
 

A transient designer could help
 
Here's a free P-Bass if yu take the midi route
http://www.amplesound.net/en/pro-pd.asp?id=19
 

Transient designer didn't work...
 
I like how the amplesound free P-Bass sounds...   I transposed it +12 but it's not right, and I can't seem to find how to get it in the right pitch.... ?
 
I record in Eb...   wonder if that is a problem?  The pitch shift worked for the SI- Bass.

You can see what any given note pitch by observing the piano keys as you hold the mouse over the note. 
 

 
So a PVR trick:
Make sure snap to grid is on so the notes don't drift out of time. 
Highlight all the notes ( CTRL A  or drag the mouse down the keyboard ) 
Now you can drag all the notes to the desired pitch. 
 
 

I think I get that part of it...
 
But why doesn't Ample Lite work the same way that SI - Bass does?   I do the exact +12 transposition, and it doesn't work. (and why do you have to transpose it anyways?)
 
I can see that when I pull the Melodyne'd bass audio clip into the Ample track, it does the conversion to midi, and the first and lowest midi note is Eb3.  Exact same as with the SI - Bass synth.  Then I try to transpose, and it does shift it to Eb2 on both Ample and SI. Hover over the midi note and it shows Eb2. But it won't sound the Eb2 on the Ample, as the keyboard display for the Ample shows that EB2 won't sound due to keyboard mapping. But the next 2 notes are wrong as well, in pitch.  ?????  wtf?  It sounds great, but seems it won't work. Dunno. 

I see they have demos so I'm downloading right now. 2.3 GB wow. Glad I'm using someone elses bandwidth :) 
 
It is a mystery why Some VST's do not use GM standard pitch. 
And it seems to be a Bass thing as well. I use a lot of Dim Pro Acoustic Bass and it also needs the +12. 
All my old midi files I made myself have to be transposed. 
 
Anyhow I will test this myself later and post. Showing 1 HR to download. 

Another cool solution if you want to use midi instruments: https://www.jamorigin.com/products/midi-bass/
 
Rocky