I made the original way too fuckin' complex. Like, holy cow, that was way too much work for a simple idea.
College of Arcana
The
college of Arcana are different from the other Bards, and broke off from
the College of Lore about three score years ago. While the College of
Lore focuses on a breadth of knowledge, the College of Arcana focuses
exclusively on the study of magic. In that study, they learn the basic
secrets of wizardly magic; not the indepth secrets of the wizard
schools, but enough that they begin to keep a spellbook and prepare
spells like a wizard, in addition to some access to bard magic.
3rd: Additional Skill
At
3rd level, College of Arcana bards receive proficiency in Arcana, or in
another skill of choice if they are already proficient. They may apply
their 3rd level Bard expertise to Arcana, even if they just learned it.
3rd: Wizard Magic
At 3rd level, Bards of the College of Arcana begin to learn spells as wizards do, in addition to their bardic magic. As Wizards, they maintain spellbooks of known Wizard spells, and may prepare their level plus Intelligence bonus in spells from their wizard spellbook, just as wizards do. Their casting attribute for wizard spells is Intelligence, so their attack bonus with wizard spells is their Intelligence Bonus + Proficiency Bonus, and the saving throw against wizard spells is 8 + Intelligence Modifier + Proficiency Bonus. They may use Wizard spellcasting focuses, and may cast wizard ritual magic (from their allowed schools) just as wizards do. They do not gain any wizard cantrips, but as they acquire more cantrips (at 4th and 10th levels), they may choose a wizard cantrip or a bard cantrip, as they wish. Wizard cantrips do not need to conform to their allowed schools.