I use to record a tube bass amp/cabinet all the time. These days I almost always blend a combination of DI, tech21 sans amp pedal and the Waves CLA Bass plugin. The blend and settings always change based on the song. I play either a US Fender P-Bass or a '70's Hofner Beatle Bass.
Mark.

Lynn
Guitar Rig 5 has a number of clean bass sounds.  I use it on all my songs these days.

Me too, there's a preset called "DI" that will get you started with a lovely chewy warm, clean tone.

I put GHS precision flats on my Jazzbass. I went for the Jazz over the P for the extra flexibility of 2 pickups and I think I lean towards the mellower tone. I love Jamersons tone also, but after many comparisons, the J-Bass seemed  better fit. I spent a year and half with the stock strings, and when my flats came, I knew they were worth the wait. Completely sits the tone in the mix to my ears.  
 
I also out GHS tapewound nylons on my acoustic. I instantly regretted it, they felt terrible, and rubbery. I was gutted. I persisted with them, and I'm glad I did, the feel and tone started to change and a day later they were like different strings. I love the tapes on the acoustic. Roundwounds seem to bring out a boxyness in the tone, and the fret noise was too much.
 
I practice more with the acoustic than the J Bass. I was worried it was a bit of a foley, but it's turned out to be a wise purchase

There were five new CA-X bass FX Chains in the August update. Give 'em a try, they're free and you've already downloaded them