DH and I just got back from holidaying in Mexico. We’ve been several times and have always hired a car to get about with no trouble being sensible, not driving at night etc.
Yesterday returning to the airport we were pulled over by a police motorbike. He accused DH of speeding (we weren’t, cars were overtaking us and we had just pulled off a roundabout). He took DHs license and said he would write a ticket for 4000 Mexican pesos (about £150). We had barely any cash on us and didn’t want to hand it over obviously but he insisted the police station was 30 minutes away and with a flight to catch we couldn’t do this. So he followed us to an ATM where DH took out some cash. We gave him some not all so we could make our flight.
Its left us both quite shaken and in hindsight a few things we would do differently - be less honest about where we were going so they didn’t think we were rushing, refuse to hand over the physical licence and make a copy, ask for the officers ID and carry a small amount of cash. We’ve since learnt that the rental company should have supplied us with some info to hand over to the office too basically saying we won’t be paying any bribes. We don’t think there’s much else we can do but please be better informed than us if you are in this situation!