No, you only pay in advance when you take the bus. When you take a cab/taxi, you set the rate in advance, but only pay at the end (when the currency is less valuable).
I still don't get it. Let's say the real price is 1 peso per mile for both services. You want to travel 100 miles. On the bus, you pay 100 pesos up front. In the taxi, the meter is set to one peso per mile. Then you pay 100 pesos at the end. Unless you are going to convert from some other good into pesos and then pay, the cost is still the same.
Inflation means that the value of 100 pesos in the future is less than the value of 100 pesos now. In countries under hyperinflation, supermarkets will raise their prices several times a day.
"During the Brazilian inflation of the earl 1990s, for instance, supermarket workers reportedly spent half of their time replacing old price stickers with new ones." -- Essentials of Economics
It only makes sense if you were going to (hypothetically) do something with the pesos. Let's say you bought 100 pesos worth of bananas when you hopped in the cab. Then, when you got out, before you paid, you sold the bananas. Because of inflation, you got more pesos for the bananas (say, 150 pesos), and still only had to pay 100. So at the end of the trip you have 50 pesos you wouldn't have had if you had to pay at the beginning (and couldn't buy your bananas).