Google removed links to my name over four years ago but Bing are refusing to do the same. They are using the 'Public interest' excuse. I have applied to the ICO but they are a waste of time just backing what Bing are saying. I know Bing has a small user base but I would like to get all links to my name removed  

Nope! Same experience as you, really. 

Once my sentence was spent Google was no issue and have been great so far moving forward for any new links that pop up etc. Bing are awful to deal with, their removal form is atrocious to use especially if you have a few links to submit (a more cynical person might think that it is intentional to turn folk off from doing it), my sentence has been spent for 3 years at this point and Bing are still having none of it still use the "public interest" with no way to appeal or even state what their criteria for this "public interest" even is! 

I also went to ICO about it and thought that given Google removed my links that could be a helpful avenue to push the case with Bing but sadly not, after waiting months and months for ICO to get back to me it essentially "No, nothing we can do lol".