Although the noise may be embarrassing, it is the odor which is a real problem as it has anonymous attribution. The noise could be eliminated by a tube which would bypass the soft tissues which vibrate to create the sound but would have to be removed for normal elimination processes.

The odor might be handled by some sort of catalytic converter to oxydize the offending gases. A more spectacular solution would be to ignite the exiting gases in a flame display which could create macho competitions as to the duration and length of the flame but one would have to be careful about creating a fire hazard and discretion would require a fire extinguisher be kept handy

I find the simplest solution is to grab one of the buttocks and pull out ward, streaching the anus to a point where it is almost or slightly open. This alows the gas to be passed with out the reverberation that causes the noise. Granted this does take some precision maneuvering but it can be perfected over time. This will not hellp with smell. Then there is always going to the restroom. If smell is a problem then this option alows some relief. When used together these two moves are very effective. Even if people are close to the restroom by useing the first technique they will not hear you and the smell is placed in a separate room where there is hopfully an exhaust fan that will get rid of the gas. For smell you may also want to carry matches.

There are charcoal filter underwear available to filter smell and a tube insert would greatly reduce sound. You can insert a whistle and startle others!

Symptom solved, perhaps, but I'm worried more about the flatulence. Seems like a dietary issue, if not a full-blown (hah!) gastric disorder.

There are pills on the market that neutralize the amount of methane produced. Perhaps it kills a certain class of bacteria, or promotes another like in Yogurt. This product is already available.