What is Widge's relationship with Simon Bass in The Shakespeare Stealer?

Widge is little more than Simon Bass's glorified servant. That's certainly how Simon sees the relationship. In his guise as Falconer, Bass gives the orders, and Widge follows them to the letter.

Technically and legally, Bass is the master and Widge his apprentice, as Bass bought his apprenticeship for the princely sum of £10 upon discovering Widge's skill at shorthand. But there's definitely more of a master/servant dynamic to their relationship than a master/apprentice one. After all, a master's supposed to teach certain skills to his apprentice. But Bass doesn't really teach Widge anything; he simply has him go off to the Globe and transcribe the dialogue of Hamlet. Bass is using Widge for underhand purposes, making him not just a servant but a co-conspirator in a criminal enterprise.

How does Widge's experience with "charactery" aid Simon Bass in The Shakespeare Stealer?

Charactery is a kind of short-hand writing. When Simon Bass discovers that Widge is very good at it, he immediately sets him to work, telling him to go to the Globe Theatre and write down Shakespeare's Hamlet word for word. Widge does as he is bid and writes down the play's dialogue in a kind of code that he will be able to transcribe into English later.

However, the task proves to be easier said than done. Widge has his pocket book stolen, the book with all the dialogue from Hamlet written in it. At his wits's end and scared stiff of what the intimidating Simon Bass might do to him, Widge feels he has no choice but to go back to the Globe and steal the original play book.