If I have a Bard in the party who is granting a +2 Bonus, and an Archaeologist who is using his Archaeologists Luck +2, do they stack to give the Archaeologist a +4 bonus?
Archaeologist's luck provides luck bonuses. So long as the bardic performance in question provides a non-luck bonus (such as inspire courage's morale bonus), any roll affected by both abilities would stack the bonuses.
Incidentally, now I'm picturing Indiana Jones navigating an ancient temple while John Williams' first chair trumpet follows him around playing the Raiders of the Lost Ark theme.