Can the red area be accessed by road? I ask NOT about Ucluelet because it can.
I do not know how, and so use purple arrows, to highlight roads on Google Maps; but please tell me if you do! All roads (e.g. Highway 14 from Victoria) appear to terminate at Port Renfrew.
Yes, you can certainly drive to Bamfield by car (which is located right around the word "Rim" in your map above). The main route takes you through Port Alberni and uses semi-public logging roads.
If you're renting a car, be sure that your insurance covers driving on these roads. I don't know for sure, but if I had to guess I would assume it does not.
Between Port Renfrew and Bamfield, you will find the West Coast Trail which is a backpacking route, and there is certainly no road that direction.
Are you using a different Google Maps than I do? The one I am using shows a lot of roads in the area -- not in the reserve itself, of course. There is even a shuttle bus going to Pachena Bay and Bamfield from May 1 to September 30. You could also fly to the Bamfield airport. 