Is there a season when it's easiest to remove bee nests? I.E. The bees are dormant?
Honey bees are different than most other kinds of bees (yellow jackets, wasps, hornets, and bumble bees): Honey bees survive in the winter by staying in their nest, consuming their honey, and huddling together to keep warm. Yellow jackets, on the other hand, have a life cycle basically of:
So first step is to identify honey bee or not.
If it's not a honey bee, then you have two choices. If it's not in a spot where you're likely to be stung and they're not really bothering you, you can just wait for the winter for them to die naturally. If you do want to eradicate the nest, then get a can of insecticide and use it late in the evening when most of the bees are in the nest. Spray it into any holes in the nest, and wear protective gear while you do this.
If it's a honey bee, and you do want to kill them, the best time is the evening, and may be easier in the late winter/early spring when there are fewer of them. It may take two or three tries to get them all, especially since the young larvae are protected by wax inside the honeycomb.
Source/more details: http://www.sembabees.org/toplevelpages/bees_in_wall.html
After you remove them, if they were in a wall or somewhere they shouldn't be, then you should figure out how they got in and seal up the holes so they can't get back. Don't seal up holes before they're gone, as otherwise they'll look for another way out, which may be to the inside of your house.
If you determine that you have honey bees (see Kate Gregory link above), find a local beekeeper group and offer the bees. Consider where the bees are. Local beekeepers should not be expected to fix walls that need to be accessed.