Think carefully before you simply resign, but I agree that you don't want to be sacked. it is an awful thing to carry on your CV.
Here's another idea - talk to a solicitor, get him/her to set up a meeting with the company and work out a compromise agreement where you (for example) resign, get a decent reference and some kind of redundancy deal/garden leave to allow you to look for another job without the worry. They might say no, but it is an easy way out for them too so may well agree.
It is not a good idea to wait to be sacked, how long it takes depends on the organisation and they have to go through the disciplinary process, they cannot simply sack you. You have to engage with them and work out a solution.
I would warn that going through the courts on a bullying complaint is soul destroying, and the outcome is never satisfactory. This is why you need good legal advice from an employment specialist solicitor.