Usually, if you are living and working for anytime in any area of Mexico you'll learn that "the mordida" is something people from out of town or foreigners have to pay to solve little problems like perhaps a traffic violation or some infraction real or imagined by the "Officer".
If you actually do live and work in an area, and speak Spanish and inter-relate with the locals -- everything is resolved through a "favor exchange". I lived and worked for 26 years in Central Mexico and do not recall paying a bribe, per se, but I do remember many times that I "fixed" problems through exchanging a favor or two between willing participants. Maybe some free Ice Cream from my Ice Cream Store in exchange for getting my electricity back from a black-out before worrying about the rest of the town? Or free Ice Cream for overlooking the fact that I drove past you while you were on foot-patrol and me and my friends were drinking Pacifico out of tins? It's all good, man.
Corruption is highly misunderstood in Canada and the US. A person can be thoroughly corrupt through-and-through and still be a good guy. Or, the next person can be thoroughly corrupt through-and-through and be a bad guy. Or even, a thoroughly corrupt person could have one foot in both worlds, always looking to the wind to see which direction the flags are blowing.
The favor exchange gets things done. It makes the wheels of a resisting bureaucracy roll, at least for you if you have the right favor to exchange or can come close enough.
On a highway miles from where you live, being pulled over by the State Highway Patrol, you'll either be paying an actual bribe or talking your way out of it with your excellent Spanish. I always succeeded with door number two. But others may have mileage that varies. I was there a long time, but that doesn't guarantee that on my next trip, I won't have to reach for the wallet. I wouldn't declare too vigorously one way or the other what might happen, it's always sort of up in the air.
With the Mexican Army, bribes are not a safe thing to attempt. They might arrest you and burn you at the stake to prove to the World they are not corrupt. Much better to find actual "work-arounds". Registering a .357 Magnum that's marked as a .38 Special with an actual .38 Special cylinder on board is a work-around. The .380 ACP problem was solved with a work-around that the Mexican Army could live with. Bribes would not have worked, although certainly some favors were exchanged.