I think that having potted herbs inside will attract bugs in my apartment. Am I worried about nothing?
If your plants are blooming by an open window, they will attract bugs, but you generally won't have a problem.
I live in Canada, so should I wait for a particular time to start growing or can I start that at any point in the year?
If you have a lighting system set up, and your apartment is heated :), it won't matter what time you plant. If you have a sunny window, starting in spring will be the most natural to the plants (some plants determine when to flower by changes in day length, so sometimes fall seedlings bolt right away).
Here are some things you need to know before growing herbs indoors:
Light. Most herbs like at least 4 hours (but often more) of direct sunlight daily. If you do not have a window with that kind of exposure, you will need to use grow lights, placed less than two feet from the plants' tops. Most people overestimate the potency of grow lights, but what looks bright indoors is usually dark in comparison with direct sunlight.
Air conditioning can be very hard on indoor herbs. The dry air and low temperatures can cause drying and premature bolting. Low humidity will also encourage spider mites.
Atmosphere. If you have a gas range, this can cause sudden deaths to your plants. Most herbs will not tolerate propane gas.
Watering indoor plants is different from watering outdoor plants. The biggest difference is the lack of rain indoors. Most people tend to water too often, and keep the mix constantly moist. You will get better results if you wait until the top layer is dry, and then water to make it count.
Dust in nature is washed off by rain. Indoors, you can use a mist sprayer, like a well cleaned out cleaner bottle. Failing to clean off dust can eventually lead to etiolation from blocked photosynthesis, but is generally seen as a general lack of vigor.
Heat vents in winter will circulate very hot, dry air, which can damage plants. The plants should be placed where the air circulation from these vents is minimum. Radiator heat is ideal.
Here are some more resources on growing herbs indoors: