In one embodiment, the gaming system enables a player to place one or more side bets on one or more outcomes associated with one or more bonus events, wherein the player participates in each of such bonus event(s) regardless of when that bonus event is triggered and regardless of which gaming device(s) in the gaming system is associated with the triggering of that bonus event. In another embodiment, the gaming system enables a player to place a side bet which is associated with an eligibility period, such as a designated period of time or a designated quantity of games played. If no bonus events are triggered during the associated eligibility period, the placed side bet is lost and the gaming system does not provide the player any bonus event awards in association with the placed side bet.