First off Tillie, well done for wanting to tackle this. Whilst many will say "that's a HR issue" and then move on the effect of workplace bullying does have consequences that fall firmly into the H&S camp, as clearly shown by the amount of info on the HSE website.

Now, whilst a questionnaire may have some effect it'll be limited. Those who are involved in bullying won't take much notice of a thinly veiled 'I know what you're doing'. The stance needs to be loud and clear that bullying, regardless of the perceived reason, will not be tolerated and action will be taken where it is witnessed. Have a conversation with HR and put together some material for general briefing as well as some material that can be displayed around the workplace. In terms of material there's plenty on the HSE website relating to workplace stress, much of which is focused on bullying.

I think the other element that needs some focus is the workplace culture that has allowed for bullying to propagate. You can tackle the problem after it has happened but prevention is better than a cure. It is important that some face to face conversations are conducted with everyone to gain an understanding why some feel it's ok to have an active role in bullying, why those not active may sit by and let it happen and why those on the receiving end do not feel they can raise the issue. The cultural factors will be key to how successful any action in the workplace is.

My final word would be that any action needs to be endorsed by your senior manager, so you'll also need to have a conversation there.

Good luck with it, not walking by is a good start to dealing with the problem.