where do I find a bigger sprocket?
First thing to do is see if your front/rear sprocket is the OEM 15/38 configuration. Some people take the 15 off the front and replace it with a 14 (I did for a while) until the chain begins to wear and the whole system can be replaced. Various ideas, but the general consensus is that the 15 front and 43 rear is the best solution for the ST4s. I've run with that for the last several years and can recommend it. Some maintain that 42 or 44 rear is better, but these are outlier opinions. The 15 front 43 rear (superlite) with the DID gold 525 chain is the best, 102 links. You might want to read this post:
http://www.ducati.ms/forums/80-hall-wisdom/28202-sprocket-gearing-recommendations.html. As already mentioned, your 6th gear system is already an overdrive. I wouldn't worry about top end, since 15/43 will already get you thrown into prison if you decide to seek out absolute speed.
You need to change the chain, the front and rear sprockets. Sprocket Center provides a good package:
525 Chain Kit - SUPERLITE RS7 Steel Sprocket Set with Your Choice of X'ring Chain - DUCATI 996 ST4S '02-05 - 996 ST4S 2002-2005 - Ducati - STREET. The Sprocket Center people fill their orders promptly and are reliable.
The DID chain comes with (if I recall) maybe 120 links, so you will need to cut some off to get to 102 links. There is no reason to go with a 520 chain when your bike is as heavy (relatively) as the ST4s. If you don't have a chain breaker/riviter, then you want to get a reasonably priced unit (
Motion Pro sells these). If you don't have some way to get the old chain off, many of us use the Dremel tool, which can be had at Home Depot. Alternatively, an angle grinder will do the job in half the time, but you want to be careful of the sparks and gas in the garage. If you haven't done this before, you will want to watch a video on UTube or Vimeo on how to replace a motorcycle chain. The Sprocket Center package comes with a master link to be riveted in, and it is easy to do if you're careful.
There is a whole friggin' mystique about working on your bike that should be set aside right away. Replacing a chain is one of the most straight-forward items of maintenance that can be imagined. Just pay attention to the process and it will be fine.
Ron
Ron
