Is threatening someone at work for bullying a fellow colleague classed as gross misconduct or give cause for instant dismissal?

Yes it can be. What I can't tell you, nor anyone else, is what your company policy's are or the consequences for breaking them.  If I was your employer, and had witnesses of your behavior, I would fire you immediately for causing a hostile work environment.  It doesn't matter what you were like before or after, threatening violence crosses a line and creates a reason to not trust you in the future from doing so again.

Yes it is gross misconduct...........

If owned a company or had hiring/firing authority I'd fire you on the spot for threatening violence to another employee and I'd give you 15 minutes to collect your personal belongings and leave the premises and would supervise you the entire time to ensure you took ONLY your personal belongings. I'd also make it clear that you are banned from company property and I would immediately call the police if you set foot on company property again. I would also appeal any claim you made for unemployment benefits.

There are ways to bring bullying and inappropriate behavior to management's attention but threatening violence against the bully is not acceptable.

I would then open a full investigation into the bullying and discipline the bullies in accordance with what I found.

Then I'd start a company wide training to ensure that everyone knows that both bullying and threats of violence will not be tolerated at my company and that everyone knows where & how to report any such issues. There would be at least 3 options for reporting such issues - each person's direct manager, as well as a senior level manager and a human resources person or to myself directly. This way nobody can use the excuse that they didn't feel safe going to the person they were supposed to report it to.

I would dismiss you.

You clearly threatened violence, even though you didn't follow through.

We don't know about your employer.

Why don't you all grow up instead of acting like 6th graders?

Remember back when everyone had to be decent at least 90 percent of the time?

"Is this grounds for dismissal?"

That's up to the discretion of your employer.