Arcane Composer

As a bard, you know that your music and works require every bit as much preparation and attention as the arcane musings of any wizard, and, inspired by them, you have learned to record your better tricks in a journal of musical notation. You gain a spell book, per the wizard feature. When you learn a new bard spell, you can additionally choose a spell from the wizard spell list of a level you can cast to record in your spell book. You can record a number of spells in your spell book in this manner equal to your Intelligence modifier, and doing so requires you to expend the resources as normal for a wizard recording spells in their spell book. 

For each level of the spell, the process takes 2 hours and costs 50 gp. The cost represents material components you expend as you experiment with the spell to master it, as well as the fine inks you need to record it. Once you have spent this time and money, you can prepare the spell just like your other spells.

At the end of a long rest, you can expend a use of your Bardic Inspiration to exchange a number of spells from your list of spells known for spells in your spell book. When you do so, choose a number of spells of 1st or higher level to exchange, up to a limit of total spell levels based on your bardic inspiration die size, as demonstrated on the chart below. Once known by you, the spells count as bard spells that you know but do not count against the number of spells you gain from the Magical Secrets feature. For example, Nostromus, a 7th level bard with 3 wizard spells recorded in her spell book - arcane eye, dispel magic, and mage armor - completes a long rest and wishes to modify her list of known spells. Her inspiration die is a d8, so she can exchange a total of 4 levels worth of spells. She can trade her 4th level charm person for arcane eye, or trade two of her 2nd level spells, such as enthrall and locate object, for arcane eye. Whatever trade she chooses to make, if any, she is now considered to know these spells as bard spells until she finishes a long rest, at which point, she reverts to her normal list of spells known. 

Any scroll of a spell on the wizard or bard spell list that you find can be recorded in your spell book, per the normal rules of the wizard feature. If you have recorded the maximum number of spells possible in your spell book based on your Intelligence modifier and find a new wizard or bard spell as a spell scroll, you can make an Intelligence (Arcana) check to copy it into your book, using the rules for a wizard attempting to copy a spell normally beyond their ability to cast.