I've cut & modifed a large cardboard box to fit over my computer. The box is lined with 2 layers of bubble wrap, has cut aways at the back for cables & fan exhaust as well as flaps for the on button & CDROM draw PLUS space all around for heat dissipation. You can also set up a frame around it & drap HEAVY blankets over the frame BUT leave space for heat dissipation.
You mentioned that you're using a soundblaster card - I started off there last year - it's something you'll need to leave behind as soon as you can - a better & dedicated card should be you next investment.
Try
http://www.homerecording.com/bbs/showthread.php?t=206291&highlight=computer+noise
or
search at
http://www.silentpcreview.com/
You're not using the "mic" in on the card are you? If Yes swap to the "stereo "line" in. that'll make a huge difference re noise.
Whatever prog you are using you should be able to mute tracks that aren't carry signal at any one time. I'm use Cakewalk Pro Audio - a few years old but I can automate faders etc to avaoid as much noise as possible.
Waverepair is a $30 download that would allow you to ( after mixing) sample the hiss from the wave file & then remove it (graduated levels of sensitivity & an option between direct & undo-able editing) from the file. there must be other progs that are wave editors etc you can down load for free.
Set up away from the comp if you can or isolate it similar to above (there should be better ideas if you do a search on the forum). make sure your pre isn't adding too much noise ( adjust the levels at the sound card as well as the pre to get a best fit - try recording an open mic whilst adjusting both & noting settings then play back to determine the best for your circumstance.
Close mic'ing, though it has it's own probs, will require less attenuation so you might get less noise by experimenting with mic placement esp for your guitar.
Remember normalising the signal inside the comp will increase all sound recorded.
As far as the bass is concerned I wouldn't add more runs etc - it's sparse but nicely so at present. Your song is working well on the less is more principal at present - don't clutter a good thing.