'Taxi bill' is not a common phrase, and we wouldn’t really say anything but ‘fare’. Like Randy said; the phrase suggests a large taxi fare. 'Taxi fare' is the better phrase to use, but they have quite a similar meaning and no-one will be confused if you say 'taxi bill' Normally a 'fare' is a small payment you make for something that you pay for at the same time as you receive the item or service. ‘Bus fare’, ‘taxi fare’. A bill is asking for payment for something you have already received. ‘Phone bill’, ‘restaurant bill’.

In that context, "taxi bill" is the same as "taxi fare", but no one says "taxi bill". Of course, if I took a taxi from New York to San Francisco, that would be a bill!