It's not inside the bellows, it's in front. I call this the stainless ring. The carbon piece (fragile part so be gentle) is clamped inside the bellows with a hose clamp on the outside of the bellows and protrudes out the front of the bellows. The carbon piece doesn't rotate and makes the water tight seal against the stainless ring which rotates with the drive shaft.
There should be some pressure provided by the rubber bellows (acts as a spring) to keep the carbon seal against the stainless ring, there should be no gap. It's not a tremendous amount of pressure, my old original one might have 2~3 pounds of pressure, my guess.
With these two parts rubbing together (note the mating surfaces are machined flat) a thin film of water from outside the hull provides lubrication. Avoid contaminating the carbon piece with oil or grease that might foul it and cause it to stick to the stainless ring.
While running on trailer more than a minute or two, these two pieces can have enough friction to become quite hot, this might tend to damage the rubber parts involved. This is primarily why I don't typically run my engine more than 30 seconds at a time while on the trailer, also I don't need cooling water for this short run time, I'm just making a quick test to determine if boat is splash worthy.
Keep in mind, my boat hasn't been more than 100 yards from water so this is my method, thus you might need to do more out of water testing than me so in that case beware the carbon seal does need some tending to such as sliding the stainless ring forward to release tension or spraying it periodically with water to keep it cool while/if running for more than a minute or two.
Under the stainless ring is a c-clip in a groove to locate the stainless ring on the drive shaft and keep it from sliding forward. You must press the stainless ring against the bellows assembly and slide it aftward on the drive shaft to reveal and remove the retainer c-clip. This is probably difficult to accomplish if the jet pump has already been removed b/c the drive shaft has nothing to keep it in place while applying force against the stainless ring while compressing the bellows and reveal the c-clip that locates (retains) the stainless ring in place.
Also inside the stainless ring, you'll find two o-rings that provide an airtight seal between the stainless ring and the drive shaft. This is a static seal (not dynamic) between the stainless ring and drive shaft that rotates with the drive shaft at the same speed, ie: stainless ring and drive shaft rotate together as an assembly.