That's great. Mine is only 3 miles if I take the car route, or 3.5 if I take the residential. I started January 1st and so far I've only missed 2 days. You might try adding the full trip back first because you can do that one more leisurely than when you are trying to get to work, maybe throw it in on Fridays first, although sometimes Monday's can be better after a full weekend of rest.
For the first 3 months or so I took the residential route, but it has this huge hill in the middle of it whereas the car route is basically flat (climb of 150ft or so), but the more annoying problem is all the stop signs in a residential area, got pulled over once for going through one; I realize that is unsafe now and don't do it which makes the residential route that much more annoying. I started taking the car route and it was sort of scary at first, but leaving at 9:30 there isn't much traffic here anyways. Now I have no problem with taking it, I've only been honked at once the whole time, cars generally just pass me when it's safe. I do feel a bit of relief when I reach the bike lanes which are on both sides of my route, but I'm not afraid to take the lane now to avoid the sewer grates and potholes which have been left near the sidewalk.
One thing that helped me was after my second day of driving a car I realized that I was trying to race myself too much, so I stopped timing my rides. I started out with barely pushing 12mph to where I can now go steady at 18-21mph on flat grounds and have no problem keeping 14mph up the hill. In comparison to your route it looks like you ride an average of 5mph, if you can get that up to 20 then your route is only 40 minutes, or 54 minutes if you get up to 15mph average. After a while of riding you'll get to know the lights and which ones you can slow down before and which ones you'll make it through. One day when riding back from the brew shop I came across the bus and I caught up to it at every stop it had to make. At best the bus will take the same amount of time, at worse it may take more.
Sometimes I wish I had a longer commute, 3 miles just seems so easy now. It's fun to go out to other places, it no longer feels like it takes so long to get there, like when I go to the brew shop on the other side of town. Ironically since I've moved I have ridden my back every time I have done to the DMV, once to get my drivers license transferred, and once to register my car.