Yup.....take the Ferry or just walk under the Harbour Channel.
The pedestrian tunnel opened in 2015 so the ferry is now mainly used by airport vehicles and those that have authority to cross. No public/passenger vehicles. Pedestrians are allowed but most are just dropped off on the mainland side.....take the elevator down to the tunnel and walk over to the airport.
It would have been nearly impossible to make the tunnel accessible to vehicles as no room is available for the length of road grade/slope required on either side to reach that depth. Even on the mainland a elevator is required to go straight down to the tunnel but there is room for the escalator bank slope on the airport side.
The Island Airport is convenient to anyone going downtown and is a competitor to VIA. There are numerous hotels within walking distance and pedestrian friendly. Just walk to/from your gate to your hotel! Trip report here: