A lot has to do with your work. How would your boss handle it if you got a flat and were 30 minutes late? If they are OK with people having car trouble, why would they get upset if you had trouble with your mode of transportation?

Another thing you can do is try to mitigate the risk of breaking down. The most common problem are flat tires. You can virtually eliminate them by getting a tough tire, like Gatorskins and using a puncture resistant tire liner. Then all you have to do is just make sure you have the correct tire pressure every 3 days or so and you will not have to worry much about flats.

Other mechanical issues can be prevented by doing your maintenance. Wash your bike, lube your chain, adjust your cables, lubricate your bearings. Don't let things fester. If you have a frayed cable, replace it. If the chain is starting to stretch, replace it. If a bearing does not feel right, replace it. While bicycles are much simpler than cars, they still require some maintenance to be reliable. Be sure to have some basic items in your saddle bag so that you can fix minor issues like something coming loose.

Ultimately, do what you think is right for you. If you don't feel comfortable with riding the whole way both ways, then take the bus to work and ride home.