How to take better pictures at bull rides?

I'm a photographer who takes pictures at a local bull ride. I currently use a nikon d3100 with a 18-55 mm lens and a 55-200 mm lens. I also use a sb-600 flash. I have been getting alot of really great shots, but I want to get the best shots that I can, all the time! I have been keeping my shutter speed high, so i can catch all the movement! However I have noticed that there are still parts of the pictures that are still blurred. Also, I have a harder time at night! Even with my flash, and my shutter speed at its max, the pictures turn out too dark. I have tried adjusting my shutter speed and the aperture, and it still only wants to work half the time, and they still turn out either too dark, blurred, etc. Does anyone have any good recommendations or tips to use? Anything would help and would be greatly appreciated! Also, any good tips on a good wide-angle lens for my camera!

Increase the ISO setting so that the shutter can work faster and the flash recycle quicker. You may get a bit more electronic noise to deal with but ISO 800 should be OK. Prefocus or manual focus 1/3d of the way into the action so it can shoot without autofocus messing around for ages.

I shot bull riding for Fox, ESPN and other sports outlets for about 10-years - all of it television.
It's apparent you already understand that your real problem is light.

All the still guys I encountered in those days from small events all the way to the NFR in Vegas, always would wire the arena ahead of time with perhaps as many as 10 flash units. When they fired a single shot that place looked like lightning had struck inside the building. Their shots were always sharp and crisp.

Now as I read between your lines that's probably not possible for you so, I agree run your ISO up but no higher than 800 because you'll probably start to get noise. If your camera has noise suppression, as does my t1i, use it to it's highest value, that will help.

These kinds of events a difficult at best - been there done that. One thing I would encourage you to do is go to an event just to experiment. Try different settings, shutter speeds, ISO speeds, apertures, etc… Try as many as you can think of.

Then keep notes of what you're doing with those settings - #128 is: etc. Now you'll have a record of what you've done and perhaps next time you can just go there and get what you want.

I don't believe you'll ever rid yourself completely of blur. There are times, as you well know, when those bully feet are moving so fast no camera can catch them in the light you've got to work with.
Bright sun perhaps, but not in arena light - it just won't happen.

You have discovered what every photographer has known for eons… Too fast a shutter speed means the focal length is too short, making parts of your photo blurry… Out of focus. Too slow a shutter speed, makes it all blurry.

What you may not know is that there's a shutter speed above which your sync with your flash will not work.

The cure, of course is a huge bazooka lens that will cost you a year's wages.

Cameras are still not as good as the human eye.

Another cure is a flash that sends out more light. This will enable you a faster shutter--- maybe. Look at the specs on the unit before you buy it. And as always, night photography in sports is always tricky, unless you are using huge lighting units, plugged into a power source.