The idea is that you are billed a nominal value, whose rate is fixed when you contract the service. Since the rate is always agreed to at the beginning of the trip, the time of payment has an impact on its value.
This joke is essentially the opposite of debt deflation (theory of recessions), as described by Irving Fisher;[1] the theory states that the debtor loses money during deflation, causing repayment problems. In the bus/taxi joke, the rider is a debtor, and the taxi driver is a creditor, with the length of the ride being the term of the loan. The inflation is essentially devaluing the loan.