According to Word of Jim, Bob made a deal for service. WOJ:
Why does Bob have to obey whoever owns his skull? Is it because of the enchantments on the skull, or is it just that all spiritual entities must obey whoever controls their sanctum?
It’s the bargain Bob made to be who he is, basically. The skull is essentially his contract–shelter in exchange for service.
Bob's service is tied to the skull because of the deal he made, evidently with Etienne the Enchanter (who may or may not have birthed him similarly to Dresden). Bonnie is under no such contract, as far as I can tell; her skull is merely a shelter Dresden gave to her willingly—much like any father would. Now, Dresden may be able to forge a new deal with Bonnie, and has hopefully learned enough about deals to make one that doesn't put Bonnie's ownership at risk, but as far as I can tell, the same restrictions don't necessarily apply to Bonnie currently.
Unless the very act of providing the skull and Bonnie using it forges a contract all on its own. It's entirely possible that, because Harry based Bonnie's skull on Bob's, part of the enchantments etched into it include a kind of binding. It may not be a conscious quid pro quo deal like you get with the Fae, so I think it might just be a coin toss about how Bonnie's service is going to work. If she's not bound, then Bonnie can play merry hell with Chicago.