How to force bonus act change in Diablo 3?

Solution 1:

The game cycles through the default bonus act (the act that has the bonus when you first make a game), once per hour.

If you want the act to change to a different one, the only way is to complete the current bonus act.

Typically, most people will complete all 5 acts (with bonuses moving between acts) at once to keep their materials fairly even. If you only need materials in particular acts, its a good idea to determine when that act becomes the default for the hour and then farm it repeatedly.

Also, as ardaozkal said in the comments, you can also join public bounty games and try to find a game with a different bonus act that's underway.