Simple, all you need to do is:
Get a Mop, any will do
Old t-shirt
Plastic bag
Duck tape
The process goes like this,
Wrap the t shirt around the head of the mop and tape it in place. Then put the t shirt and mop head into the plastic bag and duct tape like hell. Then pop the mop head with it's new covering into the bog and plung like mad. The trick is to get enough pressure by squeezing the mop head into the pan and on removal it should suck the mess out of the way. Adjust the mop t shirt rate if needed.
I did this and it actually worked only took about 10minutes and saved me a wedge on the cost of a plummer.