The way I did it and how many others do it
Get a piece of dense foam cut to the required size and insert it into the bass drum.
You want a depth of about 3" for the foam but can use less depending on the amount of damping required.
Ring is not all bad and can be part of your sound but that was not what you were asking about.
The foam needs to be wide enough to touch both heads.
Then with your prefered pedal head (felt or wood) and tuning you will be able to get that 'pro thud' or 'tight slap with punch' that you always wanted without the ring........ Nice for live work, recording or just impressing the girls ..... Female or Male type :)
My Bass Drum..... well, currently set to deep chest thud with punch....... you hear it you feel it,
You don't forget it.
This works for me!
I hit it with this stick, July 2009