Bribery is common both for Mexican border cops and city cops, they will normally settle for what they think you have so keep your bigger amount of money deep hidden so that they can just take what is in your billfold.
I used to be big on arm wrestling as a bar hustle and one of the smartest things I ever did in Mexico was after beating everyone in the packed bar of a little community that I was stuck in with a broken down car, a large but distinguished older guy (50s?) wanted to try me, from all the other men’s reactions to him I picked up on something and felt I better lose this one which I did, with a display of an epic battle that this guy barely squeaked out a win from.
He was so flattered by the hero worship he got from the crowd that he took my buddy and me to his home for drinks and his wife’s great food, which we needed since we were close to broke, well it turned out that what I picked up on was him being a retired fed, during the weeks we spent stuck there sleeping in the car while getting the stink eye from very scary looking federales who would visit him, my relationship to that guy is what saved us, I think he always knew I threw the match and was appreciative of the status it conferred onto him.
The uniformed federales that would look at me and my buddy was chilling, we kept out of the bar when they would show up and just sat in our little convertible Fiat Spider waiting for them to finish their beers and conversation with my arm wrestling buddy.
Interesting story, you should write a book. Really.