I am guessing you are talking about the Ibanez GSR-200 in your profile? I have tried one and found it actually sounded pretty good. In my opinion your biggest limiting factor is your 20watt amp. Even the nicest bass will sound a bit thin and boxy through a small amp. Try the bass through a bigger rig before deciding which one to upgrade.
If it has to be the bass then start cheap and do one thing at a time. Start by having a tech change out your pots for high quality ones. Should only cost a few bucks a pot plus labour. See if that helps.
After that there is plenty of debate on wether pickups or pre should go first. To upgrade both with new stuff will cost $300 to $400 so you are now encountering that tricky situation of "maybe I should just buy a better bass or amp".
Here is a good option I just thought of: For $100 get the Dimarzio PJ set
http://accessories.musiciansfriend.c...Set?sku=302285. The model P and model J sound fat and growly and are great wired up passive, thus: have a tech rip out the pre amp in your Ibanez and wire it up passive. The Ibanez has four pots so get them to wire it up with a volume and a tone for each pickup. (it will need different pots for passive so that solves that as well) and even with labour you should come out no worse than $200. In my opinion this will be the cheapest way to maximize the tone of your bass.
Don't worry about the bridge. The Ibanez one is fine. My AV '62 Fender Jazz with the cheesy little bent metal bridge has some of the best sustain I have heard in any bass.
EDIT: Just noticed that the GSR-200 is already passive. There you go, just have a tech drop the Dimarzio's right in and you are in business. A pot upgrade would help though. At this pricepoint upgrading the pots can make an appreciable difference.