Does the toilet always flush fine if you uase a bucket?

If the water mostly swirls around in the bowl and doesnt go down fast
check the bowls rim. hard water can clog the rim passages.

try pouring water with food cloroing down the dip tube in the tank. see
f the colored water comes out well all around. poor flow equals
sediment deposits

recently fixed a toilet broke 2 years by pouring acid down the dip
tube. dont recommend it but it worked great.

http://www.toiletology.com/index.shtml

a excellent reference