If you are wanting to send items away to be shredded and have nothing to put them into then a shredding bag is really whay you need. Things such as black bin liners tend to defeat the purpose as they can often split, which then negates the confidentiality side of shredding.
A shredding bag is not only strong but can be filled to the designated line and can be sealed. Bags can be collected or posted to you should collection is an issue. If you already have paperwork in archive cartons then there is no need to take them out of these and put them into shredding bags.
Once you have filled your shredding bags if you contact your nearest Simply Shredding branch they will be able to arrange collection.