Enjoy yourself down there! I never got the chance to climb down there but I have had lots of experience driving around the Mexico City area. The first time I drove through that city I was truly left with an adrenaline rush comparable to that of climbing. The police will always be a factor for you, especially if you have US plates or a rental car from DF. The person who paid $100 for a bribe is an idiot though. Way too much. Here's what you do. When you get pulled over (and you will) politely say you are very sorry for any infraction you may have incurred. Do not get pissed off, remain friendly no matter what. Also do not immediately offer $. They will want to have your drivers llicense. Normal procedure for an infraction in Mexico is to retain the license to ensure that you come down to the station some day to settle up. Since you will not be doing this, make sure to buy an international drivers license from AAA that you can leave with them. Also try giving them photocopies of the license. This has worked for me in the past even though they're not usually happy about it. Unlike a police encounter in America, you can completely take control of the situation in your favor down there. Eventually say you are once again very sorry and ask if you can possibly pay the fine right now. Try offering a small amount of money, no more than $10 US. After you agree on a price, act confused and lost (which you will be) and ask if he can show you out of the city in the direction you're going. I did this once and found it to be well worth the ten bucks to find my way out of that place.
If you don't speak any spanish, just skip right ahead to the confused and lost bit and speak gibberish to the cop. Try a spoken word version of "Mary had a little lamb" or something like that over and over. They will eventually just get frustrated and let you go. Also have a copy of the bible highly visible by the dashboard. Whatever you do, don't give them your license, just give them a copy, or better yet the AAA disposable one. Good luck! I'm kicking myself for never getting around to going up Popo before it became active. Also the little town of Cholula would be a real nice place to base yourself.