The problem is not so much the paper, but the chemicals used in the ink and the plastic coatings found on the paper. I have never understood why the ministry of the enviroment here uses glossy paper that is bad for the enviroment instead of easily biodegradable types.

Plastic coatings may be a problem, but almost all inks these days are biodgradable.
I tried shredding paper with a garden shredder myself, it just clogs up either type of machine. Shredded paper may be added to a compost heap as long as it is not the majority of material and it is well soaked.

I think that the first problem would be a mechanical one for the shredder. I don't think that mine would cope with it.

I have an impact shredder and as long as I roll my newspapers up nice and tight then it does work for me. I tend to use paper as a way of cleaning my machine after putting the household waste through it. I shred all my veg waste before putting it on the compost heap!

If you soak things like bank statements in water until they go mushy they will easily squelch up and go under the beans.

If you want to shred paper, Rymans sell several paper shredders which are not that expensive. The output can then go on the compost heap and will rot down quite quickly

If you grow Runner Beans, I believe that paper holds the moisture well if you bury it in the trench.