Bards can not use an Arcane Focus.
In the characteristics of the Bard class there is a "Spellcasting Focus" section that says:
You can use a musical instrument (see the Tools section) as a spell focus for your bard spells.
In addition, the description of an Arcane Approach states:
A sorcerer, sorcerer or wizard can use that element as a spell focus.
Since the bard is not included in the list of classes in the description of the Arcane Approach and the Spell Casting Focus section only mentions musical instruments, bards can not use a normal Arcane Approach.