What the descriptive element is (bolstering courage, etc), is irrelevant. What matters is the name of the bonus.
If Bless had the same description, but provided a "sacred" bonus ... then it would stack with BArdic inspiration. however, both produce a Morale bonus, so no ... no stacking. Except in very few cases, like-named bonusses do not stack.
Actually the Bards would supersede it because it has a more powerful affect by also allowing a +1 to damage as well not just the plus one to hit that the bless spell provides.