Depends on where you initiate your trip…if in Mexico, nobody will ask you for a passport. If out of Mexico, then you will be asked for it in the border.

Mikey lives in Acapulco.
If you are crossing the border by LAND then you will not need one - only a photo ID.
If however you are flying into Mexico than you will need a passport.
This law will change June next year. Mikey knows their will be a flood of applications then and that will back up the passport agency and will take longer to get one. Right now the turnaround time is the normal 2/3 weeks. Visit your local post office for all the forms and info.
You can pay an expiditer to do it for you ( around $200) and they can turn it around in about 1 week.
Here is the link for all the details.

I can only assume you are going to be taking a Mexican bus line. If so don’t sit in the back - toilets and they are not the prettiest. Enough said. The bus station in Acapulco is located in downtown ( real Acapulco ) and there are plenty of blue and white VW bug taxis to get you where your going. Please negotiate the amount before you get in. You can probably get to wherever you need to go for 50 pesos.75 on a good day and no more than 100 pesos - find another cab.
Pay attention b/c this area is what I call the real Acapulco. Not what most tourist’s see.
Here is my flicker page with some of the sights of Acapulco and the real Mexico.

Here are some other hints to the city.
The blue and white buses run the length of the bay / costera and are 4.50 pesos. Just wave them down and they will stop. Yell “baja” and they will drop you off.
Dont eat anything peddeled on the beach - enough said.
Don’t waste your time with Puerta Marquis to the south or Calleta to the north. Very small beaches and somewhat dirty.
Mikey’s favorite beach is Playa Diana - all know where it is - look for the circular water fountain with a girl on top. I like it for the rocks to add intrest and shade and to dive off of and sit on and ponder life. Oxxo is a 30 minute round trip wlk for free ice if you buy your beer there. Just help your self to the little cooler at the front of the store. Tortas Diana just behind the store to the left has the best Tacos and Tortas in town.
You must take a day and go to Pie de la Cuesta. 100 pesos for a taxi is a good price. Go all the way past the Air Force base and its runway. You will be in the middle of nowhere on a deserted beach all to yourself. Walk down one of the many allyways to the beach. Dont go swimming as the waves will kill you. Walk back towards the south and get more beer when needed up an ally way and then return to the beach. Stop and grab some lunch and then dinner and then head across the street to the lagoon to wash off the salt water and then hail another cab to get back to the noise and big city of Acapulco.
Have fun and contact me if you need anything………….