The strategy for the bonus roll is the same for the similar game Dice with buddies. In general, you should use Bonus roll with 4 of kinds going into Yahtzee bonus.

Try to get the Yahtzee via the free bonus roll during early game so that you can fill up the Yahtzee box earlier on. If you do not have good opportunities with 4 of kinds, save the free bonus roll for late game when you are finishing up the Lower section scorecards such as Large Straight.

Bonus Rolls and Player Versus Play
Save your Yahtzee with Buddies bonus rolls and only use them for tournaments to boost your scores much higher with multiple Yahtzee.

How to Get Bonus Roll in Yahzee or Dice with Buddies
Lastly, remember to gift and regift the bonus roll often to boost your bonus roll inventory. Play all the free tournaments to get free scratchers that gift you additional bonus rolls too.