Interesting topic. I remember there being some ideas a few years ago about a shuttle service or some sort of service loop that would cross back and forth between downtown Ottawa and Gatineau. Something like circling Wellington and crossing Portage to Maisonneuve, then looping back via the Alexandria Bridge down Mackenzie and back to Wellington. I think there was an idea to have shuttles running in both directions. Obviously transfers would be needed but definitely a rapid connection between one side to another with regular high frequency service. Haven't heard about it again in several years.
I think there was also another idea again in the past few years of a aerial gondola lift that would cross the river from one side to another. No news on that since as well.
While people would prefer some sort of service that offers continuing service to Gatineau, and the same from Gatineau to Ottawa, rather than a short line shuttle service, anything is better than nothing. Look at other cities, Montreal have the Yellow Line on the Metro to go to Longueuil. People take buses to Longueuil terminus and transfer to the Metro for essentially three stops to downtown Montreal and continue from there on another line or bus route.
And I think we also forget that there is A LOT of people who get off at Lebreton, walk over to the #8 route stop and take that as a shuttle to Terraces de la Chaudiere and Place du Portage. Same in the evening in the reverse direction. When this already happens and the line ups waiting for the bus to arrive can extend quite a bit, why not formalize or offer a more solid link with some sort of dedicated shuttle route (tunnel, overhead aerial gondola, or the rail bridge at Prince of Wales.
Simple solution, a shuttle that goes back and forth from Bayview to Terraces de la Chaudiere in Gatineau. There is only one track but it can be twinned at both ends of the bridge. Let's say it takes 30-45 seconds to cross one side of the bridge to the other, you could have quite decent frequency by having the tracks twinned, so as soon as it crosses it has it's own track, while the other train leaving can pass and then make use of the bridge. You could probably have 3-4 trains running simultaneously.
Anyways, just ideas to put out there and some food for thought.