Usually anything that goes into a bladder tank, comes right back out. I think it would be unusual to have sediment build up in a bladder tank. The inlet/outlet is right on the bottom, and sediment should be the first thing expelled when you draw water from the tank.
The only way to clean it would be to turn off power to the pump and drain all water from the system with a valve or faucet. The faster you let the water out, the more velocity there will be to take sediment with it. Then refill the tank with clean water and repeat until clean.
It is more likely that your bladder is busted. Then a lot of crap settles to the bottom of the tank and you start noticing stuff in the water and low pressure at start up. But you will find this out when you drain the tank as described as above. Just check the air charge while the tank is empty of water.