Question regarding insurance bad faith handling/claim

Hey Everyone,

I'm involved in a lawsuit with a former tenant on made up accusations. I am in Sacramento, CA. I was originally sued for $6.5 million and my policy is for $400k (liability insurance). My insurance said the lawsuit is absurd and were only willing to offer 40k. The claimant countered the 40k offer at $400k (right under my policy limit).

My insurance didn't even respond and didn't try to negotiate at that point. They took their chances in mediation or a trial.

When I got to the mediation the claimant raised their settlement amount to $950k. My adjuster who was with me told me told me he's only authorized to settle for 45k and I need to throw in money to try and settle this, even though I still am under my policy limits.

Now this is going to trial and I am liable for claimant attorney fees and whatever amount is over my policy limit. I feel my insurance didn't settle this when they had a chance under my policy limits.

My questions is do I have grounds for a bad faith lawsuit from my insurance company if I lose at trial. And if so, how do bad faith claims play out?

Any help would be much appreciated.