Most poker rooms count "raked hands" as any hand where you are dealt cards and where a rake is taken from the pot. Hence, with this soft rule you could hypothetically play in zero hands and still meet the requirements (only paying your blinds/antes).

Typically, there are about 60 hands dealt per hour at each full-ring table. Hence, you reach about 45 raked hands per hour at full-ring tables with the standard raked hands rule, as about 75-80% of the pots are raked (e.g. reaching the flop and minimum pot requirement for rake). To clear a standard bonus such as $100 with 10 raked hands per bonus dollar you need to reach 1,000 raked hands which you will do in about 20-25 hours if playing at one table or 10-13 hours if playing at two tables simultaneously.

Often you only have 2-3 months to clear the bonus or it will be forfeited. There is a time limit on about half of the poker bonuses available. If not, you have unlimited time to clear the bonus.

Tournament play is often completely excluded from the raked hands requirement or assessed according to a special strict formula. The reason is that the poker rooms make less money from tournament play and will not recoup their cost of the bonus as quickly. So, if there is a tough time limit, then focus on the cash games until you have cleared the bonus.

Note that at many poker rooms you are not allowed to cash out any money before the entire bonus amount is cleared, even if you have been winning a lot. If you haven't checked the policy, try to clear the full bonus before cashing out!