I use the big mesh bags for grapes, plums, etc and yes, the pulp is a mess.
I found if I clean it best I can by spraying it with water and then hanging it to dry for several days then just give it a good "snap", all the dried little bits come off. Turn it inside out and pop it again. I hold it by the corners of the bottom.
The little pieces seem to hang on tight when wet but turn loose wfter drying. You might have to scrub it between your hands a little and repeat.
The parts that are in the seam are really aggravating. Sometimes they get to stay
and are boiled to sanitize before the next use