She is avoiding the slave route and looking in more to her perspective it is really terrifying to be once a slave then be a slave again. And she doesn't know how important mages are she only know that they are needed. Imagine you escaped a toxic relationship and developing trust issues on being in a relationship again. Oh and she misunderstand a lot of stuff so.............
She thinks she murdered her master as well. So she is scared that she is a runaway slave who will be blamed for the death of her master. She is scared she will either be a slave again, or worse she will be killed.
I get the fear she has, especially since her self esteem is probably in the toilet
She's a mage, so why not just accept the offer, draft a magic contract binding your life and the king and ask for immunity and protection in exchange of you working in the palace.