such a great question.
yes it’s very important to have a business card on you to show them that you take what you do seriously.
having a profesional camera doesn’t always mean you’re a photographer - so having the camera hanging off your shoulder won’t always work.
at times models will be walking around the city and they will be in a rush to castings. dont be offended if they just say no and keep walking (it happened to me when i moved to new york last year).
if they stop and listen to you it’s important to start off with introducing yourself getting the models name & then asking “are you signed with an agency?” if the answer is yes then you ask with who and thats when you go out of your way and contact the agency and ask if she’s available to test or shoot for whatever job you’re offering.
having a stylish outfit could bring the attention to a few models- some of them don’t care. I’m not very stylish myself, but i try.
if you have your iPhone on you then great! (agency signed model or not this will work) make sure to have a folder with some of your previous shoots and show them what you have to offer.
hope this helps.