Photographing Bees

Bees are a good subject to choose as there are many around to practice on. Another good thing about photographing bees is they are usually out in the sun. This means you can get the correct exposure whilst having plenty of scope to have really fast shutter speeds to still movement.

The Honey Bee is the most common and it is large enough and slow enough for you to get some good photos. Start with photos of when the bee is on a flower and still. you can then move on to more challenging shots of bees on the wing or approaching with their tongue out.
You can then try the tiny native bees which are often fast moving. If you can find where they roost at night and catch them early morning when they are too cold to move - you can get some good shots.

Stationary on a Flower
Pick a flower with a good flat centre like a daisy or single rose. They have more pollen and nectar and the bee will stay there longer. There is also less chance of the insect being partly obscured by petals. An aperture of around f8 or higher will help you achieve a good depth of field without having to compromise on ISO or a slower shutter speed to get the correct exposure.

In Flight
Shutter speed is very important in these shots, otherwise you will just end up with a blur. Decide whether you want the body and wings still (1/800 sec or higher) or body still and wings partially blurred approx 1/200 - 1/400 sec.
Trying to focus on an incoming bee is really hard as they are relatively small and fast. Instead watch what flowers they visit and pre-focus on a flower edge and wait. Make sure your camera angle is on the same plane as the flower and approaching bee. (See below, the bee approaching the pink flowers).
Waiting takes a fair bit of patience, but if you pick a warm sunny day and there is a lot of activity, you will be rewarded.

Lenses macro vs Telephoto
You can use almost any lens, but the best option is a telephoto Macro lens eg 100mm (Olympus 60mm) or a telephoto lens that can do 200 - 600mm. Some of the modern zoom lenses allow you to focus reasonable close which means you don't have to crop the picture so much afterwards. 
The advantage of a telephoto lens is you can be further back which is less likely to spook the insect. Also, you may be able to record different behavior. See the picture of the bee flying towards the camera with the green eyes.

Tiny Bees
These bees usually only come out when it is warm or hot. Find a bush or tree with nectar rich flowers. If it is in the sun, you might find a great number of them. These are very fast moving so be patient. Wait till they land on a flower and start feeding.
You may be lucky that one will stop and clean itself and you will have time to get some good photos. If it is a little cooler, you may find them resting on branches or leaves. For these bees, it would be best to use a macro lens.

Enjoy the challenge. The results are worth it. You may even find it addictive!