There are a lot of buses going in and out of Barrhaven, public transportation should not be a problem. 95 runs every 5 minutes or so, even more frequent during rush hours. There are also express buses, but I'm not familiar with it. Check out OC Transpo for details.
Your best bet may be park-and-ride, that is, drive from where you live to the Fallowfield bus station and then take a bus. There are many buses to downtown, 95 and many express ones, e.g., 70/73/76/77.
Last year was an exception even in Canadian history You are worrying too much. I had taken school buses and had riden on public transportation, they are probably the safest kind of transportation in the city.