Try taking the body shell off first, and giving the bell a clean as any muck on it could dull the sound. Also sometimes the bell has come loose on its screw or needs to be tightened a bit. I had a non-working bell on another machine which just needed tightening up on its screw to get it ringing again. It may be that the spring that triggers the bell has become weak.
Looking at my own Skyriter it seems that to get at the spring you would 'just' need to take off the shell and the back-plate that supports the paper-support antenna, rather than taking off the entire carriage. However there are springs which are attached to the paper-bail which would need to be taken off at each end and I have not done that!
Pinging my own Skyriter bell, it is quite a small ping, and the bell itself is the smallest I have seen on any portable so far, so you might not get as much ping as other portables will sing.