If a bard takes the Moonbow Dedicate feat:
Prerequisite: Must worship Sehanine
Benefit: You gain proficiency with the shortbow, plus you can use a shortbow as an implement for divine and arcane powers. In addition, you gain a +1 feat bonus to weapon and implement damage rolls with the shortbow. Increase this bonus to +2 at 11th level and +3 at 21st level.
and then takes the Battle Song Expertise feat:
Battle Song Expertise
Benefit: You gain a +1 feat bonus to attack rolls you make with any weapon with which you have proficiency and with a wand or another item designated as a bard implement. This bonus increases to +2 at 11th level and +3 at 21st level.
You also gain a +1 feat bonus to the number of squares that you can pull, push, or slide creatures with your bard attacks and bard paragon path attacks.
Does the bard get a +1/2/3 feat bonus to implement attacks made through a shortbow?
It's obvious that the bard would receive his +1/2/3 feat bonus to weapon attacks, given that he has proficiency with the shortbow, but the Moonbow Dedicate feat does not explicitly make the shortbow a bard implement. The online character builder is not adding the feat bonus to implement attacks.
Is there a better way to do a shortbow-wielding bard?