First thing to try, decouple your subwoofer. Get an Auralex SubDude, GRAMMA or Great GRAMMA (they're all the same thing, just different sizes). That will greatly reduce the structure-borne transmission of bass. When your subwoofer makes sound, it also physically shakes. When it is not decoupled, that shaking makes the floor shake, which makes the walls shake, which make the ceiling shake, and before you know it, your whole structure is shaking in sympathy with your subwoofer, making it VERY easy to hear bass throughout the entire structure!
So decouple. That is step #1 for sure.
Decoupling should improve things, but if you have "thin" walls, it's not going to stop your neighbor from hearing your bass entirely. If you own this townhouse, you might have to get permission from your strata to make certain changes. So check with your strata before you take on any construction. Best case, you can do whatever you want. Worst case, you'll have to have a professioinal architect and a professional engineer draw up and sign off on plans for your renovation.
The easiest renovation for soundproofing, BY FAR, is to simply add a layer (or layers) of contrained layer damping over your existing drywall. The cheapest way to do this is with a product called "green glue". You can do a google search, or you can check out acoustimac.com - they have green glue for a good price.
You squirt 2-3 tubes on green glue onto each 4' x 8' sheet of drywall and stick a new layer of drywall with the green glue on it over your existing walls and ceiling. You can also use the green glue on the floor with some new plywood or OSB - althrough you'd obviously want to remove your finished floor (carpet, tile, laminate, hard wood, etc.) so that you can glue the new layer of plywood to the existing subfloor.
The cost for this is relatively low and you don't give up too much square or cubic footage. Simply adding a second layer of drywall doesn't do much for soundproofing, but the green glue is a visco-elastic polymer, meaning that it never hardens and it turns vibration into heat. Having that constrained layer of green glue is what makes this structure considerably more "sound proof". It's not an entire "room within a room", but it's somewhat closer to that idea, with the green glue separating the existing structure from your new drywall layer.
If you're willing to spend more money, but you want the same easy renovation and low loss of square footage, then check out QuietRock.com
QuietRock is a special (and quite expensive) drywall product. It is essentially a pre-made "sandwich" that has something very similar to green glue already built into the QuietRock drywall itself. QuietRock comes in several thicknesses. For bass, you'll want the thickest (and most expensive) version, which is called 545, and it's 1 3/8" thick. You can put the QuietRock directly over your existing drywall. It's the simplest install. If you want even better results, you can put Green Glue in between your existing wall and the new QuietRock drywall!
QuietRock is now owned and sold by a company called Serious Materials. They also sell QuietWood - a replacement for plywood - as well as soundproof doors, and various sealants, underlayments, glues and coatings that all deal with sound isolation. So check out quietrock.com for a lot of ideas. But keep in mind that this stuff ain't cheap (each sheet of QuietRock is about 10x the price of a regular sheet of drywall). Where you save money is on the cost of install and on saving square footage.
Finally, you could do a rather major renovation. You could take down your existing drywall to expose the studs. Make sure that everything back there is as it should be (no obvious holes, add sound reducing insulation). Then you could build that true "room within a room". Start by building a "floated" floor. You should check out Auralex.com and their soundproofing section for a beginner's education on the traditional ways of soundproofing. Use PlatFoam or U-Boats to create a "floating" floor. Then build new walls on top of that "floating" floor and a suspended ceiling or a ceiling built on top of the "floating" walls. You can use QuietRock and QuietWood in your new "room within a room" and you can use Green Glue as well.
The cost for this is high and you lose a lot of cubic footage as well. But it's the absolute best in terms of soundproofing.
As a last resort, there are the digital equalization methods. Audyssey is introducing LFC (Low Frequency Containment) as a new program into some higher end receivers and pre/pros this year. LFC basically silences the most common resonant frequencies (the ones that really shake your walls, just due to resonance). LFC then creates "replacement bass" at frequencies that are not typically resonant within most rooms. You lose accuracy and correct pitch in the bass, but for movies, you still get bass impact, but without the room resonance. I have no idea how effective it is yet or how good or bad it sounds, but at least it's an idea
Hope that helps!