Does it mean like this or this way?
Yes. Also can be "What a..." in "Вот так шутка!"="What a joke!"

What is the difference between sentences ->
Вот так надо поступать с такими пассажирами.
Так надо поступать с такими пассажирами.
"Так" is "like this" here or "This is how ...". "Everybody must interact with such passangers in this way/like this" or "This is how everybody must interact with such passangers".
"Вот" is some kind of slight enforcer here. Something like "here it is: ..." - you point on something - "Here it is how everybody must interact with such passangers".