Hammerite Kurust Rust Converter or it's equivalent. This is a surface treatments for steel based on Tannic acid, so leaves the base metal a deep navy blue.
Other maker's equivalent preparations give much the same results. Jenolite make one, also Vactan, and Aquasteel.
Loctite also make one but it's expensive though a little goes a long way. I've recently used one called Neutrarust 661 which seems to work. I thought the resulting colour was more dark brown than blue or blue-black, but the part (a wheel rim) was pretty rusty!
Getting an even coating is going to be about cleanliness – try caustic soda rinse first. Maybe an uneven coating can add to the character of the piece.
Do do a show and tell afterwards, please!