A great way to start up a conversation and grab the opportunity to share the gospel is by reading your bible in public.
In this day and age people "cannot" help themselves, if they see you reading your bible they are very likely to say something, whether positive or negative.
Either way you shouldn't feel uncomfortable in sharing your beliefs with them if they approach you.
If they do start a conversation, there is your ice breaker.
You will need a good half an hour to share the gospel as questions will come up during the sharing of it, so politely say
can i share the gospel with you, it will only take about 15-20mins, have you got this time?
If you do get the opportunity, always introduce yourself, as this is very kind and affectionate, this also allows you to find out their name, so that later on in the day you can pray for them.
I have personally had the opportunity to share the gospel many times this way.