Yes the Richmond Bridge does have a toll that you need to pay to cross the Richmond Bridge.
However the Toll that the Richmond Bridge does have is only collected when going in the southbound direction of the Richmond Bridge.
As of now it costs $7.00 for passenger cars to cross the Richmond Bridge and for Fas Trak users it's $8.00
So yes do be prepared to pay a toll when crossing the Richmond Bridge because there is a Toll Charged to cross it.
So be sure to have your money ready when crossing the Richmond Bridge.