This actually does work together. Note the text:
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.
The first part gives you a bonus to attack rolls you make with any weapon with which you have proficiency. The second gives you bonuses with wands or other bard implements.
Note that it doesn't say "weapon attack rolls." Instead, it says "attack rolls you make with any weapon." They're not the same.
Now, the rules for Weapons as Implements and vice versa:
Using a Weapon as an Implement: If an adventurer is able to use a weapon as an implement, the weapon works like a normal implement, but the adventurer uses neither the weapon’s proficiency bonus nor its nonmagical weapon properties with his or her implement powers....
When an adventurer uses a magic version of the weapon as an implement, he or she can use the magic weapon’s enhancement bonus, critical hit effects, properties, and powers. However, some magic weapons have properties and powers that work only with weapon powers (Rules Compendium 275).
You're making an attack with a weapon with which you have proficiency. You happen to be using it as an implement, but that doesn't matter- the text says you get the bonus with attack rolls made with any weapon, and you're making an attack roll with a weapon.
This issue comes up in a variety of ways in the game. For example, if you're using a Frost Shortbow, you could attach a Siberys Shard of Merciless Cold to it to do extra damage, which would work even when making an implement attack. If you're using a Weapon of Speed Shortbow, you make make a Ranged Basic Attack with it once per encounter as a minor action...even if the RBA is using the bow as an implement, not as a weapon.
There are three issues here, I think: Keywords, the two different kinds of proficiency, and permission by omission.
But before I go into those, a word: As always there are explicit features/feats/enchantments which break the rules, and that's why we call D&D an "exception-based" system: it deals in rules which apply universally unless (until) exceptions are made, so there is no need to enumerate the possible exceptions. We simply assume the rule unless told otherwise in a particular instance.
Keywords
If a power has the weapon
keyword, and only if the power has the weapon
keyword, does a weapon enchantment (enhancement bonuses and other features) apply to that power. Ditto with the implement
keyword and implement enchantments.
Proficiency and the Proficiency Bonus
"Proficiency" means that you've had training in the use of a weapon or implement, but mechanically it means totally different things whether you're talking about a weapon or an implement.
Weapon Proficiency and the Proficiency Bonus
Proficiency with a weapon means that you can add that weapon's "proficiency bonus" to attack rolls. Only weapons have proficiency bonuses, they only apply to powers with the weapon
keyword, and they have nothing to do with whether enhancement bonuses can be applied (see below for that bit).
Implements, Enhancement Bonuses, and Permission by Omission
You need to be proficient with an implement in order to add its enhancement bonus to attacks and damage with implement powers. You do not need to be proficient with a weapon in order to add its enhancement bonus to attacks and damage with weapon powers, but you don't get its proficiency bonus to the attack roll. (In either case, you can only add the enhancement bonus of one item at a time to an attack unless you have a rules exception which says otherwise.)
I arrived at this conclusion because the magic implement rules say you need to be proficient for the enhancement bonus, but the magic weapon rules don't. Permission by omission is sloppy, but has solid precedent.
Best Answer
Unfortunately the 4e character builder is correct.
The difference is between the implement and weapon keywords. Only those attacks with the weapon keyword add the proficiency bonus from your weapon. While a bow can be an excellent choice for the right kind of bard, it depends strongly on what you want to do with your bard. In this case, hyper-accuracy on the majority of your attacks is not possible.