BD1791 I have started wearing in public though and that's gone really well.
I think you are making well, first you are using it in public situations where you are more comfortable.
I think fortunately your partner is a sensitive man, and he is not rushing you.
Regarding your work, which is perhaps the most complicated step for you, I would leave it last, and I would take small steps to later have more confidence. It is reasonable to think that your partner will not want you to spend so many hours without a belt. But it is commendable that he has patience and supports you.
Another important jump is to give him the keys, and to prepare yourself mentally to receive a "no" many times. A keyholder must guarantee all the breaks that the girl NEEDS but not the ones that we want. It took me a while not to get frustrated and angry with those "no's", nobody likes to be denied things, but we have to accept that one of their functions in the relationship is to tell us no.
Regarding the metal detector, it has never happened to me, but, if it happened to me, I have always said that before the search I would discreetly tell the female security guard about the situation, calmly.
As @Megan says, if people see you act cool, they will act cool too. I am sure she will find it strange, but she will not say anything.