I am going to use mine in every situation that I used to use Mr in.
So when I have to introduce myself formally I will just say my first and second name as I never used to say Mr so and so.
Informally, if I meet someone at a party etc, obviously I will just say my first name.
At the bottom of a letter, not related to academia, I will just sign off using my name as I never used to put Mr so and so.
In terms of forms/new bank accounts etc, if they ask for a title, I will put Dr as I am one.
If someone calls me Mr I wont be correcting them by saying "actually it's Dr" (well, maybe I will if I get an obnoxious customer service person who is speaking to me like I'm stupid, tut only if they deserve it).
I think if you previously didn't use your title of Mr or Ms etc for something, then to start to use Dr for the same thing is obviously a bit show-offy.