2 for 2 infractions at border

Out of curiosity, I just looked it up (only took 2 or 3 minutes because I know what to search for), and the actual fine for speeding in Nuevo Laredo is 20 minimum wages. The minimum wage in Nuevo Laredo (Zone A) this year is 59.82/day. So if you had gone and paid your fine legitimately, you would have had to pay 1196 pesos.

But if you're going to bribe your way out of a fine, you really shouldn't give them so much. It just encourages them to target foreigners. In Morelia 50-100 pesos would probably be sufficient for simple speeding. I don't know what the going rate is in Tamaulipas, but in Michoacan and Guerrero, giving 1000 pesos to a traffic cop for a simple infraction would be ludicrous.

The actual procedure is usually that they confiscate your license, registration and/or plates, and in exchange give you a ticket. You get your confiscated item(s) back when you pay your fine. He would take you straight there because you were only passing through and would probably want your documents back right away. But technically getting a ticket doesn't mean you have to go straight to the station. Your ticket will have checkboxes to indicate what documents were surrendered, and you are allowed to circulate without them for so many days.