It depends on the club, however as a general rule, you usually pay block time, i,e from when you first taxi, to shutdown. So, in your example, you would pay a total of roughly 2 hours.
Some clubs impose restrictions on minimum number of hours if taking the aircraft for extended periods. For example, if you hired an aircraft for a weekend, you may be charged for say 5 hours flying whether or not you actually fly for those hours. Obviously if you fly more than the minumum you pay for the total hours.