The dark brotherhood bow motif page is only a part of the whole motif, if it were a whole motif it would only say something like "Crafting motif (Insert number): Dark Brotherhood, and it would not mention any single piece, like bow. But Ithink the only time you can get a whole motif (other than the racial, rare, and 2 from writ vendor) is if purchased direct from crown store/crown crates, otherwise they only come in pages. Page=1 piece, Book=Whole motive. I believe you purchased a single motif piece for only the bow, or I've been crafting and buying motifs wrong for three years.

Purple motif books have about 14 chapters...each for a specific piece of gear. So a “chests” chapter allows you to make chest pieces in the style...but they can be light chests, medium, or heavy.

The easiest way to earn the other chapters is to complete perfect sacraments...which are the guild dailies. Once your character is level 2 or 3 in the Dark Brotherhood skill line, an NPC pops up in the second room on the left as you walk into the sanctuary. He will send you to a solo instance where you are asked to murder two named NPCs. If you complete this perfectly by meeting all his conditions, the reward container has a 50/50 shot of containing a motif chapter.

You can only do one sacrament per day...but if you have multiple characters on your account you can run each of them once.

As an alternative, you can play the Dark Bro main story through the quest “signed in blood”. This awards you a costume...the shrouded armor...which isn’t quite the same, but it’s a quick and free way to get an assassin look.

If you can craft a piece (e.g., a Dark Brotherhood bow) on any character, you can use that piece at an outfit station on all your characters. There is no separate process for learning the "outfit style". Learning the motif page for that item also unlocks the outfit style for that item. If you go to an outfit station and go to Bows, you should see Dark Brotherhood bow unlocked and available for use on all your characters.